diff --git a/src/node/shell/state.ml b/src/node/shell/state.ml
index 95179d8c1..68ff5bb8b 100644
--- a/src/node/shell/state.ml
+++ b/src/node/shell/state.ml
@@ -236,6 +236,65 @@ module Operation = struct
 
 end
 
+let iter_predecessors
+    (type t)
+    (compare: t -> t -> int)
+    (predecessor: state -> t -> t option Lwt.t)
+    (date: t -> Time.t)
+    (fitness: t -> Fitness.fitness)
+    state ?max ?min_fitness ?min_date heads ~f =
+  let module Local = struct exception Exit end in
+  let pop, push =
+    (* Poor-man priority queue *)
+    let queue : t list ref = ref [] in
+    let pop () =
+      match !queue with
+      | [] -> None
+      | b :: bs -> queue := bs ; Some b in
+    let push b =
+      let rec loop = function
+        | [] -> [b]
+        | b' :: bs' as bs ->
+            let cmp = compare b b' in
+            if cmp = 0 then
+              bs
+            else if cmp < 0 then
+              b' :: loop bs'
+            else
+              b :: bs in
+      queue := loop !queue in
+    pop, push in
+  let check_count =
+    match max with
+    | None -> (fun () -> ())
+    | Some max ->
+        let cpt = ref 0 in
+        fun () ->
+          if !cpt >= max then raise Local.Exit ;
+          incr cpt in
+  let check_fitness =
+    match min_fitness with
+    | None -> (fun _ -> true)
+    | Some min_fitness ->
+        (fun b -> Fitness.compare min_fitness (fitness b) <= 0) in
+  let check_date =
+    match min_date with
+    | None -> (fun _ -> true)
+    | Some min_date ->  (fun b -> Time.compare min_date (date b) <= 0) in
+  let rec loop () =
+      match pop () with
+      | None -> return ()
+      | Some b ->
+          check_count () ;
+          f b >>= fun () ->
+          predecessor state b >>= function
+          | None -> loop ()
+          | Some p ->
+              if check_fitness p && check_date p then push p ;
+              loop () in
+    List.iter push heads ;
+    try loop () with Local.Exit -> return ()
+
 module Block = struct
 
   type shell_header = Store.shell_block_header = {
@@ -368,6 +427,28 @@ module Block = struct
       return locator
     end
 
+  let iter_predecessors =
+    let compare b1 b2 =
+      match Fitness.compare b1.shell.fitness b2.shell.fitness with
+      | 0 -> begin
+          match Time.compare b1.shell.timestamp b2.shell.timestamp with
+          | 0 -> Block_hash.compare (hash b1) (hash b2)
+          | res -> res
+        end
+      | res -> res in
+    let predecessor state b =
+      read state b.shell.predecessor >|= function
+      | None -> None
+      | Some { data } ->
+          if Block_hash.equal data.shell.predecessor b.shell.predecessor
+             && Block_hash.equal (hash b) b.shell.predecessor
+          then
+            None
+          else
+            Some data in
+    iter_predecessors compare predecessor
+      (fun b -> b.shell.timestamp) (fun b -> b.shell.fitness)
+
 end
 
 module Valid_block = struct
@@ -706,6 +787,25 @@ module Valid_block = struct
           Lwt.return vstate
   end
 
+  let iter_predecessors =
+    let compare b1 b2 =
+      match Fitness.compare b1.fitness b2.fitness with
+      | 0 -> begin
+          match Time.compare b1.timestamp b2.timestamp with
+          | 0 -> Block_hash.compare b1.hash b2.hash
+          | res -> res
+        end
+      | res -> res in
+    let predecessor state b =
+      if Block_hash.equal b.hash b.pred then
+        Lwt.return None
+      else
+        read state b.pred >|= function
+        | None | Some (Error _) -> None
+        | Some (Ok b) -> Some b in
+    iter_predecessors compare predecessor
+      (fun b -> b.timestamp) (fun b -> b.fitness)
+
 end
 
 module Blockchain = struct
diff --git a/src/node/shell/state.mli b/src/node/shell/state.mli
index 77fe642d6..9aa5dbccf 100644
--- a/src/node/shell/state.mli
+++ b/src/node/shell/state.mli
@@ -206,6 +206,22 @@ module Block : sig
   val block_locator:
     state -> int -> Block_hash.t -> Block_hash.t list tzresult Lwt.t
 
+  (** [iter_predecessors state blocks f] iter [f] on [blocks] and
+      their recursive (known) predecessors. Blocks are visited with a
+      decreasing fitness (then decreasing timestamp). If the optional
+      argument [max] is provided, the iteration is stopped after [max]
+      visited block. If [min_fitness] id provided, blocks with a
+      fitness lower than [min_fitness] are ignored. If [min_date],
+      blocks with a fitness lower than [min_date] are ignored. *)
+  val iter_predecessors:
+    state ->
+    ?max:int ->
+    ?min_fitness:Fitness.fitness ->
+    ?min_date:Time.t ->
+    block list ->
+    f:(block -> unit Lwt.t) ->
+    unit tzresult Lwt.t
+
 end
 
 (** {2 Valid block} ***********************************************************)
@@ -297,6 +313,22 @@ module Valid_block : sig
       (/à la/ Bitcoin) for the block [h]. *)
   val block_locator: state -> int -> valid_block -> Block_hash.t list Lwt.t
 
+  (** [iter_predecessors state blocks f] iter [f] on [blocks] and
+      their recursive predecessors. Blocks are visited with a
+      decreasing fitness (then decreasing timestamp). If the optional
+      argument [max] is provided, the iteration is stopped after [max]
+      visited block. If [min_fitness] id provided, blocks with a
+      fitness lower than [min_fitness] are ignored. If [min_date],
+      blocks with a fitness lower than [min_date] are ignored. *)
+  val iter_predecessors:
+    state ->
+    ?max:int ->
+    ?min_fitness:Fitness.fitness ->
+    ?min_date:Time.t ->
+    valid_block list ->
+    f:(valid_block -> unit Lwt.t) ->
+    unit tzresult Lwt.t
+
   (**/**)
 
   (* Store function to be used by the validator. *)