diff --git a/src/proto_alpha/lib_client/client_proto_args.ml b/src/proto_alpha/lib_client/client_proto_args.ml
index 1f5333d14..fc27d82a4 100644
--- a/src/proto_alpha/lib_client/client_proto_args.ml
+++ b/src/proto_alpha/lib_client/client_proto_args.ml
@@ -172,8 +172,8 @@ let storage_limit_arg =
           of letting the client decide based on a simulation"
     (parameter (fun _ s ->
          try
-           let v = Int64.of_string s in
-           assert Compare.Int64.(v >= 0L) ;
+           let v = Z.of_string s in
+           assert Compare.Z.(v >= Z.zero) ;
            return v
          with _ -> failwith "invalid storage limit (must be a positive number of bytes)"))
 
diff --git a/src/proto_alpha/lib_client/client_proto_args.mli b/src/proto_alpha/lib_client/client_proto_args.mli
index 610c9325f..f9c4079e7 100644
--- a/src/proto_alpha/lib_client/client_proto_args.mli
+++ b/src/proto_alpha/lib_client/client_proto_args.mli
@@ -15,7 +15,7 @@ val tez_sym: string
 val init_arg: (string, Proto_alpha.full) Clic.arg
 val fee_arg: (Tez.t, Proto_alpha.full) Clic.arg
 val gas_limit_arg: (Z.t option, Proto_alpha.full) Clic.arg
-val storage_limit_arg: (Int64.t option, Proto_alpha.full) Clic.arg
+val storage_limit_arg: (Z.t option, Proto_alpha.full) Clic.arg
 val arg_arg: (string, Proto_alpha.full) Clic.arg
 val source_arg: (string option, Proto_alpha.full) Clic.arg
 
diff --git a/src/proto_alpha/lib_client/client_proto_context.ml b/src/proto_alpha/lib_client/client_proto_context.ml
index 2708951a8..219e418e6 100644
--- a/src/proto_alpha/lib_client/client_proto_context.ml
+++ b/src/proto_alpha/lib_client/client_proto_context.ml
@@ -59,7 +59,7 @@ let reveal cctxt
       let contents =
         Single
           (Manager_operation { source ; fee ; counter ;
-                               gas_limit = Z.zero ; storage_limit = 0L ;
+                               gas_limit = Z.zero ; storage_limit = Z.zero ;
                                operation = Reveal src_pk }) in
       Injection.inject_operation cctxt ~chain ~block ?confirmations
         ?branch ~src_sk contents >>=? fun (oph, op, result) ->
@@ -109,7 +109,7 @@ let delegate_contract cctxt
   let operation = Delegation delegate_opt in
   Injection.inject_manager_operation
     cctxt ~chain ~block ?confirmations
-    ?branch ~source ~fee ~gas_limit:Z.zero ~storage_limit:0L
+    ?branch ~source ~fee ~gas_limit:Z.zero ~storage_limit:Z.zero
     ~src_pk ~src_sk operation >>=? fun res ->
   return res
 
diff --git a/src/proto_alpha/lib_client/client_proto_context.mli b/src/proto_alpha/lib_client/client_proto_context.mli
index bb1c91e84..739143a43 100644
--- a/src/proto_alpha/lib_client/client_proto_context.mli
+++ b/src/proto_alpha/lib_client/client_proto_context.mli
@@ -98,7 +98,7 @@ val originate_contract:
   ?branch:int ->
   fee:Tez.t ->
   ?gas_limit:Z.t ->
-  ?storage_limit:Int64.t ->
+  ?storage_limit:Z.t ->
   delegate:public_key_hash option ->
   ?delegatable:bool ->
   ?spendable:bool ->
@@ -125,7 +125,7 @@ val transfer :
   amount:Tez.t ->
   fee:Tez.t ->
   ?gas_limit:Z.t ->
-  ?storage_limit:Int64.t ->
+  ?storage_limit:Z.t ->
   unit ->
   (Kind.transaction Kind.manager Injection.result * Contract.t list) tzresult Lwt.t
 
@@ -162,4 +162,3 @@ val activate_account:
   activation_key ->
   string ->
   Kind.activate_account Injection.result tzresult Lwt.t
-
diff --git a/src/proto_alpha/lib_client/injection.ml b/src/proto_alpha/lib_client/injection.ml
index 92b95267f..db8069d07 100644
--- a/src/proto_alpha/lib_client/injection.ml
+++ b/src/proto_alpha/lib_client/injection.ml
@@ -106,15 +106,15 @@ let estimated_storage_single
     match result with
     | Applied (Transaction_result { storage_size_diff }) -> Ok storage_size_diff
     | Applied (Origination_result { storage_size_diff }) -> Ok storage_size_diff
-    | Applied Reveal_result -> Ok Int64.zero
-    | Applied Delegation_result -> Ok Int64.zero
+    | Applied Reveal_result -> Ok Z.zero
+    | Applied Delegation_result -> Ok Z.zero
     | Skipped _ -> assert false
     | Failed (_, errs) -> Alpha_environment.wrap_error (Error errs) in
   List.fold_left
     (fun acc (Internal_operation_result (_, r)) ->
        acc >>? fun acc ->
        storage_size_diff r >>? fun storage ->
-       Ok (Int64.add acc storage))
+       Ok (Z.add acc storage))
     (storage_size_diff operation_result) internal_operation_results
 
 let estimated_storage res =
@@ -125,9 +125,9 @@ let estimated_storage res =
     | Cons_result (res, rest) ->
         estimated_storage_single res >>? fun storage1 ->
         estimated_storage rest >>? fun storage2 ->
-        Ok (Int64.add storage1 storage2) in
+        Ok (Z.add storage1 storage2) in
   estimated_storage res >>? fun diff ->
-  Ok (max 0L diff)
+  Ok (max Z.zero diff)
 
 let originated_contracts_single
     (type kind)
@@ -207,14 +207,14 @@ let may_patch_limits
     : type kind. kind contents -> kind contents option = function
     | Manager_operation c
       when c.gas_limit < Z.zero || gas_limit < c.gas_limit
-           || c.storage_limit < 0L || storage_limit < c.storage_limit ->
+           || c.storage_limit < Z.zero || storage_limit < c.storage_limit ->
         let gas_limit =
           if c.gas_limit < Z.zero || gas_limit < c.gas_limit then
             gas_limit
           else
             c.gas_limit in
         let storage_limit =
-          if c.storage_limit < 0L || storage_limit < c.storage_limit then
+          if c.storage_limit < Z.zero || storage_limit < c.storage_limit then
             storage_limit
           else
             c.storage_limit in
@@ -256,17 +256,17 @@ let may_patch_limits
           else return c.gas_limit
         end >>=? fun gas_limit ->
         begin
-          if c.storage_limit < 0L || storage_limit < c.storage_limit then
+          if c.storage_limit < Z.zero || storage_limit < c.storage_limit then
             Lwt.return (estimated_storage_single result) >>=? fun storage ->
             begin
-              if Int64.equal storage 0L then
+              if Z.equal storage Z.zero then
                 cctxt#message "Estimated storage: no bytes added" >>= fun () ->
-                return 0L
+                return Z.zero
               else
                 cctxt#message
-                  "Estimated storage: %Ld bytes added (will add 20 for safety)"
-                  storage >>= fun () ->
-                return (Int64.add storage 20L)
+                  "Estimated storage: %s bytes added (will add 20 for safety)"
+                  (Z.to_string storage) >>= fun () ->
+                return (Z.add storage (Z.of_int 20))
             end
           else return c.storage_limit
         end >>=? fun storage_limit ->
@@ -349,7 +349,7 @@ let inject_operation
 
 let inject_manager_operation
     cctxt ~chain ~block ?branch ?confirmations
-    ~source ~src_pk ~src_sk ~fee ?(gas_limit = Z.minus_one) ?(storage_limit = -1L)
+    ~source ~src_pk ~src_sk ~fee ?(gas_limit = Z.minus_one) ?(storage_limit = (Z.of_int (-1)))
     (type kind) (operation : kind manager_operation)
   : (Operation_hash.t * kind Kind.manager contents *  kind Kind.manager contents_result) tzresult Lwt.t =
   Alpha_services.Contract.counter
@@ -365,7 +365,7 @@ let inject_manager_operation
       let contents =
         Cons
           (Manager_operation { source ; fee = Tez.zero ; counter ;
-                               gas_limit = Z.zero ; storage_limit = 0L ;
+                               gas_limit = Z.zero ; storage_limit = Z.zero ;
                                operation = Reveal src_pk },
            Single (Manager_operation { source ; fee ; counter = Z.succ counter ;
                                        gas_limit ; storage_limit ; operation })) in
diff --git a/src/proto_alpha/lib_client/injection.mli b/src/proto_alpha/lib_client/injection.mli
index 6e119a3be..eb13f1840 100644
--- a/src/proto_alpha/lib_client/injection.mli
+++ b/src/proto_alpha/lib_client/injection.mli
@@ -50,7 +50,7 @@ val inject_manager_operation:
   src_sk:Client_keys.sk_uri ->
   fee:Tez.t ->
   ?gas_limit:Z.t ->
-  ?storage_limit:int64 ->
+  ?storage_limit:Z.t ->
   'kind manager_operation ->
   'kind Kind.manager result tzresult Lwt.t
 
diff --git a/src/proto_alpha/lib_client/operation_result.ml b/src/proto_alpha/lib_client/operation_result.ml
index 66d20adf2..ee0351298 100644
--- a/src/proto_alpha/lib_client/operation_result.ml
+++ b/src/proto_alpha/lib_client/operation_result.ml
@@ -172,10 +172,10 @@ let pp_manager_operation_contents_and_result ppf
               Format.fprintf ppf "@,@[<hv 2>Updated storage:@ %a@]"
                 Michelson_v1_printer.print_expr expr
         end ;
-        begin if storage_size_diff <> 0L then
+        begin if storage_size_diff <> Z.zero then
             Format.fprintf ppf
-              "@,Storage size difference: %Ld bytes"
-              storage_size_diff
+              "@,Storage size difference: %s bytes"
+              (Z.to_string storage_size_diff)
         end ;
         Format.fprintf ppf
           "@,Consumed gas: %s"
@@ -197,10 +197,10 @@ let pp_manager_operation_contents_and_result ppf
               Format.fprintf ppf "@,@[<v 2>Originated contracts:@,%a@]"
                 (Format.pp_print_list Contract.pp) contracts
         end ;
-        begin if storage_size_diff <> 0L then
+        begin if storage_size_diff <> Z.zero then
             Format.fprintf ppf
-              "@,Storage size used: %Ld bytes"
-              storage_size_diff
+              "@,Storage size used: %s bytes"
+              (Z.to_string storage_size_diff)
         end ;
         Format.fprintf ppf
           "@,Consumed gas: %s"
@@ -218,13 +218,13 @@ let pp_manager_operation_contents_and_result ppf
      Fee to the baker: %s%a@,\
      Expected counter: %s@,\
      Gas limit: %s@,\
-     Storage limit: %Ld bytes"
+     Storage limit: %s bytes"
     Contract.pp source
     Client_proto_args.tez_sym
     Tez.pp fee
     (Z.to_string counter)
     (Z.to_string gas_limit)
-    storage_limit ;
+    (Z.to_string storage_limit) ;
   begin match balance_updates with
     | [] -> ()
     | balance_updates ->
diff --git a/src/proto_alpha/lib_protocol/src/alpha_context.mli b/src/proto_alpha/lib_protocol/src/alpha_context.mli
index 3d1fa5dec..74ffa7ad9 100644
--- a/src/proto_alpha/lib_protocol/src/alpha_context.mli
+++ b/src/proto_alpha/lib_protocol/src/alpha_context.mli
@@ -332,8 +332,8 @@ module Constants : sig
     block_reward: Tez.t ;
     endorsement_reward: Tez.t ;
     cost_per_byte: Tez.t ;
-    hard_storage_limit_per_operation: Int64.t ;
-    hard_storage_limit_per_block: Int64.t ;
+    hard_storage_limit_per_operation: Z.t ;
+    hard_storage_limit_per_block: Z.t ;
   }
   val parametric_encoding: parametric Data_encoding.t
   val parametric: context -> parametric
@@ -347,8 +347,8 @@ module Constants : sig
   val hard_gas_limit_per_operation: context -> Z.t
   val hard_gas_limit_per_block: context -> Z.t
   val cost_per_byte: context -> Tez.t
-  val hard_storage_limit_per_operation: context -> Int64.t
-  val hard_storage_limit_per_block: context -> Int64.t
+  val hard_storage_limit_per_operation: context -> Z.t
+  val hard_storage_limit_per_block: context -> Z.t
   val proof_of_work_threshold: context -> int64
   val dictator_pubkey: context -> Signature.Public_key.t
   val tokens_per_roll: context -> Tez.t
@@ -558,10 +558,10 @@ module Contract : sig
   type error += Operation_storage_quota_exceeded (* `Temporary *)
   type error += Storage_limit_too_high (* `Permanent *)
 
-  val set_storage_limit: context -> Int64.t -> context tzresult
+  val set_storage_limit: context -> Z.t -> context tzresult
   val set_storage_unlimited: context -> context
 
-  val used_storage_space: context -> t -> Int64.t tzresult Lwt.t
+  val used_storage_space: context -> t -> Z.t tzresult Lwt.t
   val paid_storage_space_fees: context -> t -> Tez.t tzresult Lwt.t
   val pay_for_storage_space: context -> t -> Tez.t -> context tzresult Lwt.t
 
@@ -829,7 +829,7 @@ and _ contents =
       counter: counter ;
       operation: 'kind manager_operation ;
       gas_limit: Z.t;
-      storage_limit: Int64.t;
+      storage_limit: Z.t;
     } -> 'kind Kind.manager contents
 
 and _ manager_operation =
diff --git a/src/proto_alpha/lib_protocol/src/apply.ml b/src/proto_alpha/lib_protocol/src/apply.ml
index 76b728728..c8f72f189 100644
--- a/src/proto_alpha/lib_protocol/src/apply.ml
+++ b/src/proto_alpha/lib_protocol/src/apply.ml
@@ -359,7 +359,7 @@ let apply_manager_operation_content :
                         Contract destination, Credited amount ] ;
                   originated_contracts = [] ;
                   consumed_gas = Gas.consumed ~since:before_operation ~until:ctxt ;
-                  storage_size_diff = 0L } in
+                  storage_size_diff = Z.zero } in
             return (ctxt, result, [])
         | Some script ->
             begin match parameters with
@@ -393,7 +393,7 @@ let apply_manager_operation_content :
                         Contract destination, Credited amount ] ;
                   originated_contracts ;
                   consumed_gas = Gas.consumed ~since:before_operation ~until:ctxt ;
-                  storage_size_diff = Int64.sub new_size old_size } in
+                  storage_size_diff = Z.sub new_size old_size } in
             return (ctxt, result, operations)
       end
     | Origination { manager ; delegate ; script ; preorigination ;
diff --git a/src/proto_alpha/lib_protocol/src/apply_operation_result.ml b/src/proto_alpha/lib_protocol/src/apply_operation_result.ml
index 07f564ba0..c54af4568 100644
--- a/src/proto_alpha/lib_protocol/src/apply_operation_result.ml
+++ b/src/proto_alpha/lib_protocol/src/apply_operation_result.ml
@@ -112,13 +112,13 @@ type _ successful_manager_operation_result =
         balance_updates : balance_updates ;
         originated_contracts : Contract.t list ;
         consumed_gas : Z.t ;
-        storage_size_diff : Int64.t ;
+        storage_size_diff : Z.t ;
       } -> Kind.transaction successful_manager_operation_result
   | Origination_result :
       { balance_updates : balance_updates ;
         originated_contracts : Contract.t list ;
         consumed_gas : Z.t ;
-        storage_size_diff : Int64.t ;
+        storage_size_diff : Z.t ;
       } -> Kind.origination successful_manager_operation_result
   | Delegation_result : Kind.delegation successful_manager_operation_result
 
@@ -214,7 +214,7 @@ module Manager_result = struct
            (dft "balance_updates" balance_updates_encoding [])
            (dft "originated_contracts" (list Contract.encoding) [])
            (dft "consumed_gas" z Z.zero)
-           (dft "storage_size_diff" int64 0L))
+           (dft "storage_size_diff" z Z.zero))
       ~iselect:
         (function
           | Internal_operation_result
@@ -251,7 +251,7 @@ module Manager_result = struct
            (dft "balance_updates" balance_updates_encoding [])
            (dft "originated_contracts" (list Contract.encoding) [])
            (dft "consumed_gas" z Z.zero)
-           (dft "storage_size_diff" int64 0L))
+           (dft "storage_size_diff" z Z.zero))
       ~iselect:
         (function
           | Internal_operation_result
diff --git a/src/proto_alpha/lib_protocol/src/apply_operation_result.mli b/src/proto_alpha/lib_protocol/src/apply_operation_result.mli
index 10842b4be..8e581a9a7 100644
--- a/src/proto_alpha/lib_protocol/src/apply_operation_result.mli
+++ b/src/proto_alpha/lib_protocol/src/apply_operation_result.mli
@@ -90,13 +90,13 @@ and _ successful_manager_operation_result =
         balance_updates : balance_updates ;
         originated_contracts : Contract.t list ;
         consumed_gas : Z.t ;
-        storage_size_diff : Int64.t ;
+        storage_size_diff : Z.t ;
       } -> Kind.transaction successful_manager_operation_result
   | Origination_result :
       { balance_updates : balance_updates ;
         originated_contracts : Contract.t list ;
         consumed_gas : Z.t ;
-        storage_size_diff : Int64.t ;
+        storage_size_diff : Z.t ;
       } -> Kind.origination successful_manager_operation_result
   | Delegation_result : Kind.delegation successful_manager_operation_result
 
diff --git a/src/proto_alpha/lib_protocol/src/constants_repr.ml b/src/proto_alpha/lib_protocol/src/constants_repr.ml
index 4b0aeaf82..4e5fb272d 100644
--- a/src/proto_alpha/lib_protocol/src/constants_repr.ml
+++ b/src/proto_alpha/lib_protocol/src/constants_repr.ml
@@ -71,8 +71,8 @@ type parametric = {
   block_reward: Tez_repr.t ;
   endorsement_reward: Tez_repr.t ;
   cost_per_byte: Tez_repr.t ;
-  hard_storage_limit_per_operation: Int64.t ;
-  hard_storage_limit_per_block: Int64.t ;
+  hard_storage_limit_per_operation: Z.t ;
+  hard_storage_limit_per_block: Z.t ;
 }
 
 let default = {
@@ -104,8 +104,8 @@ let default = {
   endorsement_security_deposit = Tez_repr.(mul_exn one 64) ;
   block_reward = Tez_repr.(mul_exn one 16) ;
   endorsement_reward = Tez_repr.(mul_exn one 2) ;
-  hard_storage_limit_per_operation = 60_000L ;
-  hard_storage_limit_per_block = 1_000_000L ;
+  hard_storage_limit_per_operation = Z.of_int 60_000 ;
+  hard_storage_limit_per_block = Z.of_int 1_000_000 ;
   cost_per_byte = Tez_repr.of_mutez_exn 1_000L ;
 }
 
@@ -207,8 +207,8 @@ let parametric_encoding =
           (obj4
              (req "endorsement_reward" Tez_repr.encoding)
              (req "cost_per_byte" Tez_repr.encoding)
-             (req "hard_storage_limit_per_operation" int64)
-             (req "hard_storage_limit_per_block" int64))))
+             (req "hard_storage_limit_per_operation" z)
+             (req "hard_storage_limit_per_block" z))))
 
 type t = {
   fixed : fixed ;
diff --git a/src/proto_alpha/lib_protocol/src/contract_storage.ml b/src/proto_alpha/lib_protocol/src/contract_storage.ml
index 7b8842eb6..7d8219856 100644
--- a/src/proto_alpha/lib_protocol/src/contract_storage.ml
+++ b/src/proto_alpha/lib_protocol/src/contract_storage.ml
@@ -189,17 +189,17 @@ let failwith msg = fail (Failure msg)
 type big_map_diff = (string * Script_repr.expr option) list
 
 let update_script_big_map c contract = function
-  | None -> return (c, 0L)
+  | None -> return (c, Z.zero)
   | Some diff ->
       fold_left_s (fun (c, total) (key, value) ->
           match value with
           | None ->
               Storage.Contract.Big_map.remove (c, contract) key >>=? fun (c, freed) ->
-              return (c, Int64.sub total (Int64.of_int freed))
+              return (c, Z.sub total (Z.of_int freed))
           | Some v ->
               Storage.Contract.Big_map.init_set (c, contract) key v >>=? fun (c, size_diff) ->
-              return (c, Int64.add total (Int64.of_int size_diff)))
-        (c, 0L) diff
+              return (c, Z.add total (Z.of_int size_diff)))
+        (c, Z.zero) diff
 
 let create_base c contract
     ~balance ~manager ~delegate ?script ~spendable ~delegatable =
@@ -222,8 +222,8 @@ let create_base c contract
        Storage.Contract.Code.init c contract code >>=? fun (c, code_size) ->
        Storage.Contract.Storage.init c contract storage >>=? fun (c, storage_size) ->
        update_script_big_map c contract big_map_diff >>=? fun (c, big_map_size) ->
-       let total_size = Int64.add (Int64.add (Int64.of_int code_size) (Int64.of_int storage_size)) big_map_size in
-       assert Compare.Int64.(total_size >= 0L) ;
+       let total_size = Z.add (Z.add (Z.of_int code_size) (Z.of_int storage_size)) big_map_size in
+       assert Compare.Z.(total_size >= Z.zero) ;
        Storage.Contract.Used_storage_space.init c contract total_size >>=? fun c ->
        Storage.Contract.Paid_storage_space_fees.init c contract Tez_repr.zero
    | None ->
@@ -388,7 +388,7 @@ let update_script_storage c contract storage big_map_diff =
   update_script_big_map c contract big_map_diff >>=? fun (c, big_map_size_diff) ->
   Storage.Contract.Storage.set c contract storage >>=? fun (c, size_diff) ->
   Storage.Contract.Used_storage_space.get c contract >>=? fun previous_size ->
-  let new_size = Int64.add previous_size (Int64.add big_map_size_diff (Int64.of_int size_diff)) in
+  let new_size = Z.add previous_size (Z.add big_map_size_diff (Z.of_int size_diff)) in
   Storage.Contract.Used_storage_space.set c contract new_size
 
 let spend_from_script c contract amount =
@@ -458,7 +458,7 @@ let init c =
 
 let used_storage_space c contract =
   Storage.Contract.Used_storage_space.get_option c contract >>=? function
-  | None -> return 0L
+  | None -> return Z.zero
   | Some fees -> return fees
 
 let paid_storage_space_fees c contract =
diff --git a/src/proto_alpha/lib_protocol/src/contract_storage.mli b/src/proto_alpha/lib_protocol/src/contract_storage.mli
index 3e45575f4..ed6d03802 100644
--- a/src/proto_alpha/lib_protocol/src/contract_storage.mli
+++ b/src/proto_alpha/lib_protocol/src/contract_storage.mli
@@ -102,7 +102,7 @@ val originated_from_current_nonce :
 val init:
   Raw_context.t -> Raw_context.t tzresult Lwt.t
 
-val used_storage_space: Raw_context.t -> Contract_repr.t -> Int64.t tzresult Lwt.t
+val used_storage_space: Raw_context.t -> Contract_repr.t -> Z.t tzresult Lwt.t
 val paid_storage_space_fees: Raw_context.t -> Contract_repr.t -> Tez_repr.t tzresult Lwt.t
 val pay_for_storage_space: Raw_context.t -> Contract_repr.t -> Tez_repr.t -> Raw_context.t tzresult Lwt.t
 
diff --git a/src/proto_alpha/lib_protocol/src/fees.ml b/src/proto_alpha/lib_protocol/src/fees.ml
index 03239b815..e1b4cfaee 100644
--- a/src/proto_alpha/lib_protocol/src/fees.ml
+++ b/src/proto_alpha/lib_protocol/src/fees.ml
@@ -28,7 +28,7 @@ let origination_burn c ~payer contract =
   Contract.spend_from_script c payer origination_burn >>=? fun c ->
   Contract.used_storage_space c contract >>=? fun size ->
   let cost_per_byte = Constants.cost_per_byte c in
-  Lwt.return (Tez.(cost_per_byte *? size)) >>=? fun fees ->
+  Lwt.return (Tez.(cost_per_byte *? (Z.to_int64 size))) >>=? fun fees ->
   trace Cannot_pay_storage_fee
     (Contract.spend_from_script c payer fees >>=? fun c ->
      Contract.pay_for_storage_space c contract fees) >>=? fun c ->
@@ -38,7 +38,7 @@ let update_script_storage c ~payer contract =
   Contract.paid_storage_space_fees c contract >>=? fun paid_fees ->
   Contract.used_storage_space c contract >>=? fun size ->
   let cost_per_byte = Constants.cost_per_byte c in
-  Lwt.return (Tez.(cost_per_byte *? size)) >>=? fun fees ->
+  Lwt.return (Tez.(cost_per_byte *? (Z.to_int64 size))) >>=? fun fees ->
   match Tez.(fees -? paid_fees) with
   | Error _ ->
       (* Previously paid fees are greater than required fees. *)
diff --git a/src/proto_alpha/lib_protocol/src/fees.mli b/src/proto_alpha/lib_protocol/src/fees.mli
index 91116aebb..3ac308718 100644
--- a/src/proto_alpha/lib_protocol/src/fees.mli
+++ b/src/proto_alpha/lib_protocol/src/fees.mli
@@ -13,9 +13,8 @@ type error += Cannot_pay_storage_fee
 
 val origination_burn:
   Alpha_context.t -> payer:Contract.t ->
-  Contract.t -> (Alpha_context.t * Int64.t * Tez.t) tzresult Lwt.t
+  Contract.t -> (Alpha_context.t * Z.t * Tez.t) tzresult Lwt.t
 
 val update_script_storage:
   Alpha_context.t -> payer:Contract.t ->
-  Contract.t -> (Alpha_context.t * Int64.t * Tez.t) tzresult Lwt.t
-
+  Contract.t -> (Alpha_context.t * Z.t * Tez.t) tzresult Lwt.t
diff --git a/src/proto_alpha/lib_protocol/src/helpers_services.ml b/src/proto_alpha/lib_protocol/src/helpers_services.ml
index da3414eaf..37018eb11 100644
--- a/src/proto_alpha/lib_protocol/src/helpers_services.ml
+++ b/src/proto_alpha/lib_protocol/src/helpers_services.ml
@@ -278,7 +278,7 @@ module Forge = struct
     let reveal ctxt
         block ~branch ~source ~sourcePubKey ~counter ~fee () =
       operations ctxt block ~branch ~source ~sourcePubKey ~counter ~fee
-        ~gas_limit:Z.zero ~storage_limit:0L []
+        ~gas_limit:Z.zero ~storage_limit:Z.zero []
 
     let transaction ctxt
         block ~branch ~source ?sourcePubKey ~counter
@@ -310,7 +310,7 @@ module Forge = struct
     let delegation ctxt
         block ~branch ~source ?sourcePubKey ~counter ~fee delegate =
       operations ctxt block ~branch ~source ?sourcePubKey ~counter ~fee
-        ~gas_limit:Z.zero ~storage_limit:0L
+        ~gas_limit:Z.zero ~storage_limit:Z.zero
         [Manager (Delegation delegate)]
 
   end
diff --git a/src/proto_alpha/lib_protocol/src/helpers_services.mli b/src/proto_alpha/lib_protocol/src/helpers_services.mli
index 94a92bbbd..4cb24117c 100644
--- a/src/proto_alpha/lib_protocol/src/helpers_services.mli
+++ b/src/proto_alpha/lib_protocol/src/helpers_services.mli
@@ -67,7 +67,7 @@ module Forge : sig
       counter:counter ->
       fee:Tez.t ->
       gas_limit:Z.t ->
-      storage_limit:Int64.t ->
+      storage_limit:Z.t ->
       packed_manager_operation list -> MBytes.t shell_tzresult Lwt.t
 
     val reveal:
@@ -89,7 +89,7 @@ module Forge : sig
       destination:Contract.t ->
       ?parameters:Script.expr ->
       gas_limit:Z.t ->
-      storage_limit:Int64.t ->
+      storage_limit:Z.t ->
       fee:Tez.t ->
       unit -> MBytes.t shell_tzresult Lwt.t
 
@@ -106,7 +106,7 @@ module Forge : sig
       ?delegatePubKey: public_key_hash ->
       ?script:Script.t ->
       gas_limit:Z.t ->
-      storage_limit:Int64.t ->
+      storage_limit:Z.t ->
       fee:Tez.t->
       unit -> MBytes.t shell_tzresult Lwt.t
 
diff --git a/src/proto_alpha/lib_protocol/src/operation_repr.ml b/src/proto_alpha/lib_protocol/src/operation_repr.ml
index f0cee7ff1..22f318a72 100644
--- a/src/proto_alpha/lib_protocol/src/operation_repr.ml
+++ b/src/proto_alpha/lib_protocol/src/operation_repr.ml
@@ -89,7 +89,7 @@ and _ contents =
       counter: counter ;
       operation: 'kind manager_operation ;
       gas_limit: Z.t;
-      storage_limit: Int64.t;
+      storage_limit: Z.t;
     } -> 'kind Kind.manager contents
 
 and _ manager_operation =
@@ -474,7 +474,7 @@ module Encoding = struct
        (req "fee" Tez_repr.encoding)
        (req "counter" z)
        (req "gas_limit" z)
-       (req "storage_limit" int64))
+       (req "storage_limit" z))
 
   let extract
       (type kind)
diff --git a/src/proto_alpha/lib_protocol/src/operation_repr.mli b/src/proto_alpha/lib_protocol/src/operation_repr.mli
index 622b5ebcd..df6053d72 100644
--- a/src/proto_alpha/lib_protocol/src/operation_repr.mli
+++ b/src/proto_alpha/lib_protocol/src/operation_repr.mli
@@ -90,7 +90,7 @@ and _ contents =
       counter: counter ;
       operation: 'kind manager_operation ;
       gas_limit: Z.t;
-      storage_limit: Int64.t;
+      storage_limit: Z.t;
     } -> 'kind Kind.manager contents
 
 and _ manager_operation =
diff --git a/src/proto_alpha/lib_protocol/src/parameters_repr.ml b/src/proto_alpha/lib_protocol/src/parameters_repr.ml
index 34530276f..fcca1d7c4 100644
--- a/src/proto_alpha/lib_protocol/src/parameters_repr.ml
+++ b/src/proto_alpha/lib_protocol/src/parameters_repr.ml
@@ -100,10 +100,10 @@ let constants_encoding =
          opt Tez_repr.(=)
            default.cost_per_byte c.cost_per_byte
        and hard_storage_limit_per_operation =
-         opt Compare.Int64.(=)
+         opt Compare.Z.(=)
            default.hard_storage_limit_per_operation c.hard_storage_limit_per_operation
        and hard_storage_limit_per_block =
-         opt Compare.Int64.(=)
+         opt Compare.Z.(=)
            default.hard_storage_limit_per_block c.hard_storage_limit_per_block
        in
        (( preserved_cycles,
@@ -223,8 +223,8 @@ let constants_encoding =
           (obj4
              (opt "endorsement_reward" Tez_repr.encoding)
              (opt "cost_per_byte" Tez_repr.encoding)
-             (opt "hard_storage_limit_per_operation" int64)
-             (opt "hard_storage_limit_per_block" int64))))
+             (opt "hard_storage_limit_per_operation" z)
+             (opt "hard_storage_limit_per_block" z))))
 
 let encoding =
   let open Data_encoding in
diff --git a/src/proto_alpha/lib_protocol/src/raw_context.ml b/src/proto_alpha/lib_protocol/src/raw_context.ml
index ea1523456..c141271b4 100644
--- a/src/proto_alpha/lib_protocol/src/raw_context.ml
+++ b/src/proto_alpha/lib_protocol/src/raw_context.ml
@@ -22,7 +22,7 @@ type t = {
   rewards: Tez_repr.t ;
   block_gas: Z.t ;
   operation_gas: Gas_limit_repr.t ;
-  block_storage: Int64.t ;
+  block_storage: Z.t ;
   operation_storage: Storage_limit_repr.t ;
   origination_nonce: Contract_repr.origination_nonce option ;
   internal_nonce: int ;
@@ -174,8 +174,8 @@ let () =
     (fun () -> Storage_limit_too_high)
 
 let set_storage_limit ctxt remaining =
-  if Compare.Int64.(remaining > ctxt.constants.hard_storage_limit_per_operation)
-  || Compare.Int64.(remaining < 0L)then
+  if Compare.Z.(remaining > ctxt.constants.hard_storage_limit_per_operation)
+  || Compare.Z.(remaining < Z.zero)then
     error Storage_limit_too_high
   else
     ok { ctxt with operation_storage = Limited { remaining } }
@@ -509,7 +509,7 @@ module type T = sig
 
   val consume_gas: context -> Gas_limit_repr.cost -> context tzresult
 
-  val record_bytes_stored: context -> Int64.t -> context tzresult
+  val record_bytes_stored: context -> Z.t -> context tzresult
 
   val description: context Storage_description.t
 
diff --git a/src/proto_alpha/lib_protocol/src/raw_context.mli b/src/proto_alpha/lib_protocol/src/raw_context.mli
index 4dee452fd..f906519f3 100644
--- a/src/proto_alpha/lib_protocol/src/raw_context.mli
+++ b/src/proto_alpha/lib_protocol/src/raw_context.mli
@@ -88,7 +88,7 @@ val block_gas_level: t -> Z.t
 
 type error += Storage_limit_too_high (* `Permanent *)
 
-val set_storage_limit: t -> Int64.t -> t tzresult
+val set_storage_limit: t -> Z.t -> t tzresult
 val set_storage_unlimited: t -> t
 
 type error += Undefined_operation_nonce (* `Permanent *)
@@ -184,7 +184,7 @@ module type T = sig
 
   (** Internally used in {!Storage_functors} to consume storage from
       within a view. *)
-  val record_bytes_stored: context -> Int64.t -> context tzresult
+  val record_bytes_stored: context -> Z.t -> context tzresult
 
   val description: context Storage_description.t
 
diff --git a/src/proto_alpha/lib_protocol/src/storage.ml b/src/proto_alpha/lib_protocol/src/storage.ml
index 46e0f9169..c5eacf536 100644
--- a/src/proto_alpha/lib_protocol/src/storage.ml
+++ b/src/proto_alpha/lib_protocol/src/storage.ml
@@ -24,11 +24,6 @@ module Z = struct
   let encoding = Data_encoding.z
 end
 
-module Int64 = struct
-  type t = Int64.t
-  let encoding = Data_encoding.int64
-end
-
 module Int_index = struct
   type t = int
   let path_length = 1
@@ -202,7 +197,7 @@ module Contract = struct
   module Used_storage_space =
     Indexed_context.Make_map
       (struct let name = ["used_bytes"] end)
-      (Int64)
+      (Z)
 
   module Roll_list =
     Indexed_context.Make_map
diff --git a/src/proto_alpha/lib_protocol/src/storage.mli b/src/proto_alpha/lib_protocol/src/storage.mli
index e27cce0e4..1e88942de 100644
--- a/src/proto_alpha/lib_protocol/src/storage.mli
+++ b/src/proto_alpha/lib_protocol/src/storage.mli
@@ -176,7 +176,7 @@ module Contract : sig
       Includes code, global storage and big map elements. *)
   module Used_storage_space : Indexed_data_storage
     with type key = Contract_repr.t
-     and type value = Int64.t
+     and type value = Z.t
      and type t := Raw_context.t
 
   (** Total fees burnt for storage space. *)
diff --git a/src/proto_alpha/lib_protocol/src/storage_functors.ml b/src/proto_alpha/lib_protocol/src/storage_functors.ml
index a118c24b4..b4bf3b886 100644
--- a/src/proto_alpha/lib_protocol/src/storage_functors.ml
+++ b/src/proto_alpha/lib_protocol/src/storage_functors.ml
@@ -359,13 +359,13 @@ module Make_indexed_carbonated_data_storage
     consume_write_gas C.set s i v >>=? fun (s, bytes) ->
     C.set s (name i) bytes >>=? fun t ->
     let size_diff = MBytes.length bytes - prev_size in
-    Lwt.return (C.record_bytes_stored t (Int64.of_int size_diff)) >>=? fun t ->
+    Lwt.return (C.record_bytes_stored t (Z.of_int size_diff)) >>=? fun t ->
     return (C.project t, size_diff)
   let init s i v =
     consume_write_gas C.init s i v >>=? fun (s, bytes) ->
     C.init s (name i) bytes >>=? fun t ->
     let size = MBytes.length bytes in
-    Lwt.return (C.record_bytes_stored t (Int64.of_int size)) >>=? fun t ->
+    Lwt.return (C.record_bytes_stored t (Z.of_int size)) >>=? fun t ->
     return (C.project t, size)
   let init_set s i v =
     let init_set s i v = C.init_set s i v >>= return in
@@ -373,20 +373,20 @@ module Make_indexed_carbonated_data_storage
     consume_write_gas init_set s i v >>=? fun (s, bytes) ->
     init_set s (name i) bytes >>=? fun t ->
     let size_diff = MBytes.length bytes - prev_size in
-    Lwt.return (C.record_bytes_stored t (Int64.of_int size_diff)) >>=? fun t ->
+    Lwt.return (C.record_bytes_stored t (Z.of_int size_diff)) >>=? fun t ->
     return (C.project t, size_diff)
   let remove s i =
     let remove s i = C.remove s i >>= return in
     existing_size s i >>=? fun prev_size ->
     consume_remove_gas remove s i >>=? fun s ->
     remove s (name i) >>=? fun t ->
-    Lwt.return (C.record_bytes_stored t (Int64.of_int ~-prev_size)) >>=? fun t ->
+    Lwt.return (C.record_bytes_stored t (Z.of_int ~-prev_size)) >>=? fun t ->
     return (C.project t, prev_size)
   let delete s i =
     existing_size s i >>=? fun prev_size ->
     consume_remove_gas C.delete s i >>=? fun s ->
     C.delete s (name i) >>=? fun t ->
-    Lwt.return (C.record_bytes_stored t (Int64.of_int ~-prev_size)) >>=? fun t ->
+    Lwt.return (C.record_bytes_stored t (Z.of_int ~-prev_size)) >>=? fun t ->
     return (C.project t, prev_size)
   let set_option s i v =
     match v with
@@ -784,13 +784,13 @@ module Make_indexed_subcontext (C : Raw_context.T) (I : INDEX)
       consume_write_gas Raw_context.set (pack s i) v >>=? fun (c, bytes) ->
       Raw_context.set c data_name bytes >>=? fun c ->
       let size_diff = MBytes.length bytes - prev_size in
-      Lwt.return (Raw_context.record_bytes_stored c (Int64.of_int size_diff)) >>=? fun c ->
+      Lwt.return (Raw_context.record_bytes_stored c (Z.of_int size_diff)) >>=? fun c ->
       return (Raw_context.project c, size_diff)
     let init s i v =
       consume_write_gas Raw_context.init (pack s i) v >>=? fun (c, bytes) ->
       Raw_context.init c data_name bytes >>=? fun c ->
       let size = MBytes.length bytes in
-      Lwt.return (Raw_context.record_bytes_stored c (Int64.of_int size)) >>=? fun c ->
+      Lwt.return (Raw_context.record_bytes_stored c (Z.of_int size)) >>=? fun c ->
       return (Raw_context.project c, size)
     let init_set s i v =
       let init_set c k v = Raw_context.init_set c k v >>= return in
@@ -798,20 +798,20 @@ module Make_indexed_subcontext (C : Raw_context.T) (I : INDEX)
       consume_write_gas init_set (pack s i) v >>=? fun (c, bytes) ->
       init_set c data_name bytes >>=? fun c ->
       let size_diff = MBytes.length bytes - prev_size in
-      Lwt.return (Raw_context.record_bytes_stored c (Int64.of_int size_diff)) >>=? fun c ->
+      Lwt.return (Raw_context.record_bytes_stored c (Z.of_int size_diff)) >>=? fun c ->
       return (Raw_context.project c, size_diff)
     let remove s i =
       let remove c k = Raw_context.remove c k >>= return in
       existing_size (pack s i) >>=? fun prev_size ->
       consume_remove_gas remove (pack s i) >>=? fun c ->
       remove c data_name >>=? fun c ->
-      Lwt.return (Raw_context.record_bytes_stored c (Int64.of_int ~-prev_size)) >>=? fun c ->
+      Lwt.return (Raw_context.record_bytes_stored c (Z.of_int ~-prev_size)) >>=? fun c ->
       return (Raw_context.project c, prev_size)
     let delete s i =
       existing_size (pack s i) >>=? fun prev_size ->
       consume_remove_gas Raw_context.delete (pack s i) >>=? fun c ->
       Raw_context.delete c data_name >>=? fun c ->
-      Lwt.return (Raw_context.record_bytes_stored c (Int64.of_int ~-prev_size)) >>=? fun c ->
+      Lwt.return (Raw_context.record_bytes_stored c (Z.of_int ~-prev_size)) >>=? fun c ->
       return (Raw_context.project c, prev_size)
     let set_option s i v =
       match v with
diff --git a/src/proto_alpha/lib_protocol/src/storage_limit_repr.ml b/src/proto_alpha/lib_protocol/src/storage_limit_repr.ml
index 8584cdf1b..c2b0b62fe 100644
--- a/src/proto_alpha/lib_protocol/src/storage_limit_repr.ml
+++ b/src/proto_alpha/lib_protocol/src/storage_limit_repr.ml
@@ -9,7 +9,7 @@
 
 type t =
   | Unaccounted
-  | Limited of { remaining : Int64.t }
+  | Limited of { remaining : Z.t }
 
 type error += Block_quota_exceeded (* `Temporary *)
 type error += Operation_quota_exceeded (* `Temporary *)
@@ -41,11 +41,11 @@ let consume block_storage operation_storage ~bytes = match operation_storage wit
   | Unaccounted -> ok (block_storage, Unaccounted)
   | Limited { remaining } ->
       let remaining =
-        Int64.sub remaining bytes in
+        Z.sub remaining bytes in
       let block_remaining =
-        Int64.sub block_storage bytes in
-      if Compare.Int64.(remaining < 0L)
+        Z.sub block_storage bytes in
+      if Compare.Z.(remaining < Z.zero)
       then error Operation_quota_exceeded
-      else if Compare.Int64.(block_remaining < 0L)
+      else if Compare.Z.(block_remaining < Z.zero)
       then error Block_quota_exceeded
       else ok (block_remaining, Limited { remaining })
diff --git a/src/proto_alpha/lib_protocol/src/storage_limit_repr.mli b/src/proto_alpha/lib_protocol/src/storage_limit_repr.mli
index 11dc00af2..d52220901 100644
--- a/src/proto_alpha/lib_protocol/src/storage_limit_repr.mli
+++ b/src/proto_alpha/lib_protocol/src/storage_limit_repr.mli
@@ -9,9 +9,9 @@
 
 type t =
   | Unaccounted
-  | Limited of { remaining : Int64.t }
+  | Limited of { remaining : Z.t }
 
 type error += Block_quota_exceeded (* `Temporary *)
 type error += Operation_quota_exceeded (* `Temporary *)
 
-val consume : Int64.t -> t -> bytes:Int64.t -> (Int64.t * t) tzresult
+val consume : Z.t -> t -> bytes:Z.t -> (Z.t * t) tzresult
diff --git a/src/proto_alpha/lib_protocol/test/helpers/block.mli b/src/proto_alpha/lib_protocol/test/helpers/block.mli
index 1e57e4957..5b95bcb9e 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/block.mli
+++ b/src/proto_alpha/lib_protocol/test/helpers/block.mli
@@ -81,8 +81,8 @@ val genesis:
   ?block_reward:Tez_repr.tez ->
   ?endorsement_reward:Tez_repr.tez ->
   ?cost_per_byte: Tez_repr.t ->
-  ?hard_storage_limit_per_operation: Int64.t ->
-  ?hard_storage_limit_per_block: Int64.t ->
+  ?hard_storage_limit_per_operation: Z.t ->
+  ?hard_storage_limit_per_block: Z.t ->
   ?commitments:Commitment_repr.t list ->
   ?security_deposit_ramp_up_cycles: int option ->
   ?no_reward_cycles: int option ->
diff --git a/src/proto_alpha/lib_protocol/test/helpers/op.ml b/src/proto_alpha/lib_protocol/test/helpers/op.ml
index 689ca83e9..63156c956 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/op.ml
+++ b/src/proto_alpha/lib_protocol/test/helpers/op.ml
@@ -76,7 +76,7 @@ let manager_operation
           counter ;
           operation = Reveal public_key ;
           gas_limit = Z.of_int 20 ;
-          storage_limit = 0L ;
+          storage_limit = Z.zero ;
         } in
       let op =
         Manager_operation {
@@ -104,7 +104,7 @@ let revelation ctxt public_key =
              counter ;
              operation = Reveal public_key ;
              gas_limit = Z.of_int 20 ;
-             storage_limit = 0L ;
+             storage_limit = Z.zero ;
            })) in
   return @@ sign account.sk ctxt sop
 
diff --git a/src/proto_alpha/lib_protocol/test/helpers/op.mli b/src/proto_alpha/lib_protocol/test/helpers/op.mli
index b826de12d..ec16c9bf2 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/op.mli
+++ b/src/proto_alpha/lib_protocol/test/helpers/op.mli
@@ -23,7 +23,7 @@ val miss_signed_endorsement:
 val transaction:
   ?fee:Tez.tez ->
   ?gas_limit:Z.t ->
-  ?storage_limit:int64 ->
+  ?storage_limit:Z.t ->
   ?parameters:Script.lazy_expr ->
   Context.t ->
   Contract.t ->
@@ -50,7 +50,7 @@ val origination:
   ?credit:Tez.tez ->
   ?fee:Tez.tez ->
   ?gas_limit:Z.t ->
-  ?storage_limit:int64 ->
+  ?storage_limit:Z.t ->
   Context.t ->
   Contract.contract ->
   (Operation.packed * Contract.contract) tzresult Lwt.t