diff --git a/src/lib_protocol_environment/sigs/v1/z.mli b/src/lib_protocol_environment/sigs/v1/z.mli
index f0633b8f0..2c060554b 100644
--- a/src/lib_protocol_environment/sigs/v1/z.mli
+++ b/src/lib_protocol_environment/sigs/v1/z.mli
@@ -13,6 +13,9 @@ type t
 val zero: t
 val one: t
 
+val succ: t -> t
+(** Returns its argument plus one. *)
+
 val abs: t -> t
 (** Absolute value. *)
 
diff --git a/src/proto_alpha/lib_client/client_proto_context.ml b/src/proto_alpha/lib_client/client_proto_context.ml
index acc470c14..2708951a8 100644
--- a/src/proto_alpha/lib_client/client_proto_context.ml
+++ b/src/proto_alpha/lib_client/client_proto_context.ml
@@ -49,7 +49,7 @@ let reveal cctxt
     ?branch ~source ~src_pk ~src_sk ~fee () =
   Alpha_services.Contract.counter
     cctxt (chain, block) source >>=? fun pcounter ->
-  let counter = Int32.succ pcounter in
+  let counter = Z.succ pcounter in
   Alpha_services.Contract.manager_key
     cctxt (chain, block) source >>=? fun (_, key) ->
   match key with
@@ -319,4 +319,3 @@ let activate_account
       (Activate_account _ as op, result) ->
       return (oph, op, result)
   | _ -> .
-
diff --git a/src/proto_alpha/lib_client/injection.ml b/src/proto_alpha/lib_client/injection.ml
index 29bb0e51a..92b95267f 100644
--- a/src/proto_alpha/lib_client/injection.ml
+++ b/src/proto_alpha/lib_client/injection.ml
@@ -354,7 +354,7 @@ let inject_manager_operation
   : (Operation_hash.t * kind Kind.manager contents *  kind Kind.manager contents_result) tzresult Lwt.t =
   Alpha_services.Contract.counter
     cctxt (chain, block) source >>=? fun pcounter ->
-  let counter = Int32.succ pcounter in
+  let counter = Z.succ pcounter in
   Alpha_services.Contract.manager_key
     cctxt (chain, block) source >>=? fun (_, key) ->
   let is_reveal : type kind. kind manager_operation -> bool = function
@@ -367,7 +367,7 @@ let inject_manager_operation
           (Manager_operation { source ; fee = Tez.zero ; counter ;
                                gas_limit = Z.zero ; storage_limit = 0L ;
                                operation = Reveal src_pk },
-           Single (Manager_operation { source ; fee ; counter = Int32.succ counter ;
+           Single (Manager_operation { source ; fee ; counter = Z.succ counter ;
                                        gas_limit ; storage_limit ; operation })) in
       inject_operation cctxt ~chain ~block ?confirmations
         ?branch ~src_sk contents >>=? fun (oph, op, result) ->
@@ -387,4 +387,3 @@ let inject_manager_operation
       | Single_and_result (Manager_operation _ as op, result) ->
           return (oph, op, result)
       | _ -> assert false (* Grrr... *)
-
diff --git a/src/proto_alpha/lib_client/operation_result.ml b/src/proto_alpha/lib_client/operation_result.ml
index c44de504f..66d20adf2 100644
--- a/src/proto_alpha/lib_client/operation_result.ml
+++ b/src/proto_alpha/lib_client/operation_result.ml
@@ -216,13 +216,13 @@ let pp_manager_operation_contents_and_result ppf
     "@[<v 0>@[<v 2>Manager signed operations:@,\
      From: %a@,\
      Fee to the baker: %s%a@,\
-     Expected counter: %ld@,\
+     Expected counter: %s@,\
      Gas limit: %s@,\
      Storage limit: %Ld bytes"
     Contract.pp source
     Client_proto_args.tez_sym
     Tez.pp fee
-    counter
+    (Z.to_string counter)
     (Z.to_string gas_limit)
     storage_limit ;
   begin match balance_updates with
diff --git a/src/proto_alpha/lib_protocol/src/alpha_context.mli b/src/proto_alpha/lib_protocol/src/alpha_context.mli
index 732cb6f9e..3d1fa5dec 100644
--- a/src/proto_alpha/lib_protocol/src/alpha_context.mli
+++ b/src/proto_alpha/lib_protocol/src/alpha_context.mli
@@ -519,7 +519,7 @@ module Contract : sig
   val get_storage:
     context -> contract -> (context * Script.expr option) tzresult Lwt.t
 
-  val get_counter: context -> contract -> int32 tzresult Lwt.t
+  val get_counter: context -> contract -> Z.t tzresult Lwt.t
   val get_balance:
     context -> contract -> Tez.t tzresult Lwt.t
 
@@ -569,7 +569,7 @@ module Contract : sig
     context -> contract -> context tzresult Lwt.t
 
   val check_counter_increment:
-    context -> contract -> int32 -> unit tzresult Lwt.t
+    context -> contract -> Z.t -> unit tzresult Lwt.t
 
   module Big_map : sig
     val mem:
@@ -851,7 +851,7 @@ and _ manager_operation =
   | Delegation :
       Signature.Public_key_hash.t option -> Kind.delegation manager_operation
 
-and counter = Int32.t
+and counter = Z.t
 
 type 'kind internal_operation = {
   source: Contract.contract ;
diff --git a/src/proto_alpha/lib_protocol/src/contract_services.ml b/src/proto_alpha/lib_protocol/src/contract_services.ml
index 6587a0996..453a13875 100644
--- a/src/proto_alpha/lib_protocol/src/contract_services.ml
+++ b/src/proto_alpha/lib_protocol/src/contract_services.ml
@@ -17,7 +17,7 @@ type info = {
   balance: Tez.t ;
   spendable: bool ;
   delegate: bool * public_key_hash option ;
-  counter: int32 ;
+  counter: counter ;
   script: Script.t option ;
 }
 
@@ -40,7 +40,7 @@ let info_encoding =
        (req "setable" bool)
        (opt "value" Signature.Public_key_hash.encoding))
     (opt "script" Script.encoding)
-    (req "counter" int32)
+    (req "counter" n)
 
 module S = struct
 
@@ -80,7 +80,7 @@ module S = struct
     RPC_service.get_service
       ~description: "Access the counter of a contract, if any."
       ~query: RPC_query.empty
-      ~output: int32
+      ~output: z
       RPC_path.(custom_root /: Contract.rpc_arg / "counter")
 
   let spendable =
diff --git a/src/proto_alpha/lib_protocol/src/contract_services.mli b/src/proto_alpha/lib_protocol/src/contract_services.mli
index 599cfdcda..bdb11e51b 100644
--- a/src/proto_alpha/lib_protocol/src/contract_services.mli
+++ b/src/proto_alpha/lib_protocol/src/contract_services.mli
@@ -17,7 +17,7 @@ type info = {
   balance: Tez.t ;
   spendable: bool ;
   delegate: bool * public_key_hash option ;
-  counter: int32 ;
+  counter: counter ;
   script: Script.t option ;
 }
 
@@ -48,7 +48,7 @@ val is_spendable:
   'a #RPC_context.simple -> 'a -> Contract.t -> bool shell_tzresult Lwt.t
 
 val counter:
-  'a #RPC_context.simple -> 'a -> Contract.t -> int32 shell_tzresult Lwt.t
+  'a #RPC_context.simple -> 'a -> Contract.t -> counter shell_tzresult Lwt.t
 
 val script:
   'a #RPC_context.simple -> 'a -> Contract.t -> Script.t shell_tzresult Lwt.t
diff --git a/src/proto_alpha/lib_protocol/src/contract_storage.ml b/src/proto_alpha/lib_protocol/src/contract_storage.ml
index 3908576c2..7b8842eb6 100644
--- a/src/proto_alpha/lib_protocol/src/contract_storage.ml
+++ b/src/proto_alpha/lib_protocol/src/contract_storage.ml
@@ -9,8 +9,8 @@
 
 type error +=
   | Balance_too_low of Contract_repr.contract * Tez_repr.t * Tez_repr.t (* `Temporary *)
-  | Counter_in_the_past of Contract_repr.contract * int32 * int32 (* `Branch *)
-  | Counter_in_the_future of Contract_repr.contract * int32 * int32 (* `Temporary *)
+  | Counter_in_the_past of Contract_repr.contract * Z.t * Z.t (* `Branch *)
+  | Counter_in_the_future of Contract_repr.contract * Z.t * Z.t (* `Temporary *)
   | Unspendable_contract of Contract_repr.contract (* `Permanent *)
   | Non_existing_contract of Contract_repr.contract (* `Temporary *)
   | Empty_implicit_contract of Signature.Public_key_hash.t (* `Temporary *)
@@ -54,13 +54,15 @@ let () =
     ~description:"An operation assumed a contract counter in the future"
     ~pp:(fun ppf (contract, exp, found) ->
         Format.fprintf ppf
-          "Counter %ld not yet reached for contract %a (expected %ld)"
-          found Contract_repr.pp contract exp)
+          "Counter %s not yet reached for contract %a (expected %s)"
+          (Z.to_string found)
+          Contract_repr.pp contract
+          (Z.to_string exp))
     Data_encoding.
       (obj3
          (req "contract" Contract_repr.encoding)
-         (req "expected" int32)
-         (req "found" int32))
+         (req "expected" z)
+         (req "found" z))
     (function Counter_in_the_future (c, x, y) -> Some (c, x, y) | _ -> None)
     (fun (c, x, y) -> Counter_in_the_future (c, x, y)) ;
   register_error_kind
@@ -70,13 +72,15 @@ let () =
     ~description:"An operation assumed a contract counter in the past"
     ~pp:(fun ppf (contract, exp, found) ->
         Format.fprintf ppf
-          "Counter %ld already used for contract %a (expected %ld)"
-          found Contract_repr.pp contract exp)
+          "Counter %s already used for contract %a (expected %s)"
+          (Z.to_string found)
+          Contract_repr.pp contract
+          (Z.to_string exp))
     Data_encoding.
       (obj3
          (req "contract" Contract_repr.encoding)
-         (req "expected" int32)
-         (req "found" int32))
+         (req "expected" z)
+         (req "found" z))
     (function Counter_in_the_past (c, x, y) -> Some (c, x, y) | _ -> None)
     (fun (c, x, y) -> Counter_in_the_past (c, x, y)) ;
   register_error_kind
@@ -200,7 +204,7 @@ let update_script_big_map c contract = function
 let create_base c contract
     ~balance ~manager ~delegate ?script ~spendable ~delegatable =
   (match Contract_repr.is_implicit contract with
-   | None -> return 0l
+   | None -> return Z.zero
    | Some _ -> Storage.Contract.Global_counter.get c) >>=? fun counter ->
   Storage.Contract.Balance.init c contract balance >>=? fun c ->
   Storage.Contract.Manager.init c contract (Manager_repr.Hash manager) >>=? fun c ->
@@ -292,19 +296,19 @@ let originated_from_current_nonce ~since: ctxt_since ~until: ctxt_until =
 
 let check_counter_increment c contract counter =
   Storage.Contract.Counter.get c contract >>=? fun contract_counter ->
-  let expected = Int32.succ contract_counter in
-  if Compare.Int32.(expected = counter)
+  let expected = Z.succ contract_counter in
+  if Compare.Z.(expected = counter)
   then return ()
-  else if Compare.Int32.(expected > counter) then
+  else if Compare.Z.(expected > counter) then
     fail (Counter_in_the_past (contract, expected, counter))
   else
     fail (Counter_in_the_future (contract, expected, counter))
 
 let increment_counter c contract =
   Storage.Contract.Global_counter.get c >>=? fun global_counter ->
-  Storage.Contract.Global_counter.set c (Int32.succ global_counter) >>=? fun c ->
+  Storage.Contract.Global_counter.set c (Z.succ global_counter) >>=? fun c ->
   Storage.Contract.Counter.get c contract >>=? fun contract_counter ->
-  Storage.Contract.Counter.set c contract (Int32.succ contract_counter)
+  Storage.Contract.Counter.set c contract (Z.succ contract_counter)
 
 let get_script c contract =
   Storage.Contract.Code.get_option c contract >>=? fun (c, code) ->
@@ -450,7 +454,7 @@ let spend c contract amount =
   else spend_from_script c contract amount
 
 let init c =
-  Storage.Contract.Global_counter.init c 0l
+  Storage.Contract.Global_counter.init c Z.zero
 
 let used_storage_space c contract =
   Storage.Contract.Used_storage_space.get_option c contract >>=? function
diff --git a/src/proto_alpha/lib_protocol/src/contract_storage.mli b/src/proto_alpha/lib_protocol/src/contract_storage.mli
index b755fe9ef..3e45575f4 100644
--- a/src/proto_alpha/lib_protocol/src/contract_storage.mli
+++ b/src/proto_alpha/lib_protocol/src/contract_storage.mli
@@ -9,8 +9,8 @@
 
 type error +=
   | Balance_too_low of Contract_repr.contract * Tez_repr.t * Tez_repr.t (* `Temporary *)
-  | Counter_in_the_past of Contract_repr.contract * int32 * int32 (* `Branch *)
-  | Counter_in_the_future of Contract_repr.contract * int32 * int32 (* `Temporary *)
+  | Counter_in_the_past of Contract_repr.contract * Z.t * Z.t (* `Branch *)
+  | Counter_in_the_future of Contract_repr.contract * Z.t * Z.t (* `Temporary *)
   | Unspendable_contract of Contract_repr.contract (* `Permanent *)
   | Non_existing_contract of Contract_repr.contract (* `Temporary *)
   | Empty_implicit_contract of Signature.Public_key_hash.t (* `Temporary *)
@@ -30,7 +30,7 @@ val must_be_allocated: Raw_context.t -> Contract_repr.t -> unit tzresult Lwt.t
 val list: Raw_context.t -> Contract_repr.t list Lwt.t
 
 val check_counter_increment:
-  Raw_context.t -> Contract_repr.t -> int32 -> unit tzresult Lwt.t
+  Raw_context.t -> Contract_repr.t -> Z.t -> unit tzresult Lwt.t
 
 val increment_counter:
   Raw_context.t -> Contract_repr.t -> Raw_context.t tzresult Lwt.t
@@ -53,7 +53,7 @@ val reveal_manager_key:
   Raw_context.t tzresult Lwt.t
 
 val get_balance: Raw_context.t -> Contract_repr.t -> Tez_repr.t tzresult Lwt.t
-val get_counter: Raw_context.t -> Contract_repr.t -> int32 tzresult Lwt.t
+val get_counter: Raw_context.t -> Contract_repr.t -> Z.t tzresult Lwt.t
 
 val get_script:
   Raw_context.t -> Contract_repr.t -> (Raw_context.t * Script_repr.t option) tzresult Lwt.t
diff --git a/src/proto_alpha/lib_protocol/src/helpers_services.mli b/src/proto_alpha/lib_protocol/src/helpers_services.mli
index a7733bde9..94a92bbbd 100644
--- a/src/proto_alpha/lib_protocol/src/helpers_services.mli
+++ b/src/proto_alpha/lib_protocol/src/helpers_services.mli
@@ -64,7 +64,7 @@ module Forge : sig
       branch:Block_hash.t ->
       source:Contract.t ->
       ?sourcePubKey:public_key ->
-      counter:int32 ->
+      counter:counter ->
       fee:Tez.t ->
       gas_limit:Z.t ->
       storage_limit:Int64.t ->
@@ -75,7 +75,7 @@ module Forge : sig
       branch:Block_hash.t ->
       source:Contract.t ->
       sourcePubKey:public_key ->
-      counter:int32 ->
+      counter:counter ->
       fee:Tez.t ->
       unit -> MBytes.t shell_tzresult Lwt.t
 
@@ -84,7 +84,7 @@ module Forge : sig
       branch:Block_hash.t ->
       source:Contract.t ->
       ?sourcePubKey:public_key ->
-      counter:int32 ->
+      counter:counter ->
       amount:Tez.t ->
       destination:Contract.t ->
       ?parameters:Script.expr ->
@@ -98,7 +98,7 @@ module Forge : sig
       branch:Block_hash.t ->
       source:Contract.t ->
       ?sourcePubKey:public_key ->
-      counter:int32 ->
+      counter:counter ->
       managerPubKey:public_key_hash ->
       balance:Tez.t ->
       ?spendable:bool ->
@@ -115,7 +115,7 @@ module Forge : sig
       branch:Block_hash.t ->
       source:Contract.t ->
       ?sourcePubKey:public_key ->
-      counter:int32 ->
+      counter:counter ->
       fee:Tez.t ->
       public_key_hash option ->
       MBytes.t shell_tzresult Lwt.t
diff --git a/src/proto_alpha/lib_protocol/src/main.ml b/src/proto_alpha/lib_protocol/src/main.ml
index 8a6901802..e99b32595 100644
--- a/src/proto_alpha/lib_protocol/src/main.ml
+++ b/src/proto_alpha/lib_protocol/src/main.ml
@@ -245,13 +245,13 @@ let compare_operations op1 op2 =
 
   (* Manager operations with smaller counter are pre-validated first. *)
   | Single (Manager_operation op1), Single (Manager_operation op2) ->
-      Int32.compare op1.counter op2.counter
+      Z.compare op1.counter op2.counter
   | Cons (Manager_operation op1, _), Single (Manager_operation op2) ->
-      Int32.compare op1.counter op2.counter
+      Z.compare op1.counter op2.counter
   | Single (Manager_operation op1), Cons (Manager_operation op2, _) ->
-      Int32.compare op1.counter op2.counter
+      Z.compare op1.counter op2.counter
   | Cons (Manager_operation op1, _), Cons (Manager_operation op2, _) ->
-      Int32.compare op1.counter op2.counter
+      Z.compare op1.counter op2.counter
 
 let init ctxt block_header =
   let level = block_header.Block_header.level in
diff --git a/src/proto_alpha/lib_protocol/src/operation_repr.ml b/src/proto_alpha/lib_protocol/src/operation_repr.ml
index 92d4c4f96..f0cee7ff1 100644
--- a/src/proto_alpha/lib_protocol/src/operation_repr.ml
+++ b/src/proto_alpha/lib_protocol/src/operation_repr.ml
@@ -111,7 +111,7 @@ and _ manager_operation =
   | Delegation :
       Signature.Public_key_hash.t option -> Kind.delegation manager_operation
 
-and counter = Int32.t
+and counter = Z.t
 
 let manager_kind : type kind. kind manager_operation -> kind Kind.manager =
   function
@@ -472,7 +472,7 @@ module Encoding = struct
     (obj5
        (req "source" Contract_repr.encoding)
        (req "fee" Tez_repr.encoding)
-       (req "counter" int32)
+       (req "counter" z)
        (req "gas_limit" z)
        (req "storage_limit" int64))
 
diff --git a/src/proto_alpha/lib_protocol/src/operation_repr.mli b/src/proto_alpha/lib_protocol/src/operation_repr.mli
index 09daa5f2b..622b5ebcd 100644
--- a/src/proto_alpha/lib_protocol/src/operation_repr.mli
+++ b/src/proto_alpha/lib_protocol/src/operation_repr.mli
@@ -112,7 +112,7 @@ and _ manager_operation =
   | Delegation :
       Signature.Public_key_hash.t option -> Kind.delegation manager_operation
 
-and counter = Int32.t
+and counter = Z.t
 
 type 'kind internal_operation = {
   source: Contract_repr.contract ;
diff --git a/src/proto_alpha/lib_protocol/src/storage.ml b/src/proto_alpha/lib_protocol/src/storage.ml
index 568eaa832..46e0f9169 100644
--- a/src/proto_alpha/lib_protocol/src/storage.ml
+++ b/src/proto_alpha/lib_protocol/src/storage.ml
@@ -19,6 +19,11 @@ module Int32 = struct
   let encoding = Data_encoding.int32
 end
 
+module Z = struct
+  type t = Z.t
+  let encoding = Data_encoding.z
+end
+
 module Int64 = struct
   type t = Int64.t
   let encoding = Data_encoding.int64
@@ -84,7 +89,7 @@ module Contract = struct
     Make_single_data_storage
       (Raw_context)
       (struct let name = ["global_counter"] end)
-      (Int32)
+      (Z)
 
   module Indexed_context =
     Make_indexed_subcontext
@@ -158,7 +163,7 @@ module Contract = struct
   module Counter =
     Indexed_context.Make_map
       (struct let name = ["counter"] end)
-      (Int32)
+      (Z)
 
   module Code =
     Indexed_context.Make_carbonated_map
diff --git a/src/proto_alpha/lib_protocol/src/storage.mli b/src/proto_alpha/lib_protocol/src/storage.mli
index dfd55a551..e27cce0e4 100644
--- a/src/proto_alpha/lib_protocol/src/storage.mli
+++ b/src/proto_alpha/lib_protocol/src/storage.mli
@@ -90,9 +90,9 @@ module Contract : sig
       module `Contract`. *)
 
   module Global_counter : sig
-    val get : Raw_context.t -> int32 tzresult Lwt.t
-    val set : Raw_context.t -> int32 -> Raw_context.t tzresult Lwt.t
-    val init : Raw_context.t -> int32 -> Raw_context.t tzresult Lwt.t
+    val get : Raw_context.t -> Z.t tzresult Lwt.t
+    val set : Raw_context.t -> Z.t -> Raw_context.t tzresult Lwt.t
+    val init : Raw_context.t -> Z.t -> Raw_context.t tzresult Lwt.t
   end
 
   (** The domain of alive contracts *)
@@ -159,7 +159,7 @@ module Contract : sig
 
   module Counter : Indexed_data_storage
     with type key = Contract_repr.t
-     and type value = int32
+     and type value = Z.t
      and type t := Raw_context.t
 
   module Code : Non_iterable_indexed_carbonated_data_storage
diff --git a/src/proto_alpha/lib_protocol/test/helpers/context.mli b/src/proto_alpha/lib_protocol/test/helpers/context.mli
index a93174f6a..7557976af 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/context.mli
+++ b/src/proto_alpha/lib_protocol/test/helpers/context.mli
@@ -38,7 +38,7 @@ module Contract : sig
       deposit, fees ot rewards. *)
   val balance: ?kind:balance_kind -> t -> Contract.t -> Tez.t tzresult Lwt.t
 
-  val counter: t -> Contract.t -> int32 tzresult Lwt.t
+  val counter: t -> Contract.t -> Z.t tzresult Lwt.t
   val manager: t -> Contract.t -> Account.t tzresult Lwt.t
   val is_manager_key_revealed: t -> Contract.t -> bool tzresult Lwt.t
 
diff --git a/src/proto_alpha/lib_protocol/test/helpers/op.ml b/src/proto_alpha/lib_protocol/test/helpers/op.ml
index 283c57604..689ca83e9 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/op.ml
+++ b/src/proto_alpha/lib_protocol/test/helpers/op.ml
@@ -55,7 +55,7 @@ let manager_operation
   Context.Contract.counter ctxt source >>=? fun counter ->
   Context.Contract.manager ctxt source >>=? fun account ->
   let public_key = Option.unopt ~default:account.pk public_key in
-  let counter = Int32.succ counter in
+  let counter = Z.succ counter in
   Context.Contract.is_manager_key_revealed ctxt source >>=? function
   | true ->
       let op =
@@ -82,7 +82,7 @@ let manager_operation
         Manager_operation {
           source ;
           fee ;
-          counter = Int32.succ counter ;
+          counter = Z.succ counter ;
           operation ;
           gas_limit ;
           storage_limit ;
@@ -94,7 +94,7 @@ let revelation ctxt public_key =
   let source = Contract.implicit_contract pkh in
   Context.Contract.counter ctxt source >>=? fun counter ->
   Context.Contract.manager ctxt source >>=? fun account ->
-  let counter = Int32.succ counter in
+  let counter = Z.succ counter in
   let sop =
     Contents_list
       (Single