diff --git a/app/hurl.ml b/app/hurl.ml
index efb135b..4ce6167 100644
--- a/app/hurl.ml
+++ b/app/hurl.ml
@@ -1,10 +1,11 @@
-let jump () protocol uri meth headers output input no_follow =
+let jump () protocol uri meth headers input output no_follow =
   let ( let* ) = Result.bind in
   let config = match protocol with
     | None -> None
     | Some `HTTP_1_1 -> Some (`HTTP_1_1 Httpaf.Config.default)
     | Some `H2 -> Some (`H2 H2.Config.default)
   in
+  let open Lwt.Infix in
   let* body, default_meth =
     match input with
     | None -> Ok (None, `GET)
@@ -13,23 +14,31 @@ let jump () protocol uri meth headers output input no_follow =
       Ok (Some d, `POST)
   in
   let meth = match meth with None -> default_meth | Some x -> x in
-  let open Lwt.Infix in
-  Lwt_main.run ((
-    Http_lwt_client.one_request ?config ~meth ~headers ?body ~follow_redirect:(not no_follow) uri >|= function
-    | Ok (resp, body) ->
-      Format.fprintf Format.std_formatter "%a\n%!"
-        Http_lwt_client.pp_response resp;
-      (match body with
-       | None -> Ok ()
-       | Some data ->
-         match output with
-         | None -> Format.fprintf Format.std_formatter "%s\n%!" data ; Ok ()
-         | Some fn -> Bos.OS.File.write (Fpath.v fn) data)
-    | Error `Msg msg as e ->
-      Logs.err (fun m -> m "error %s" msg);
-      e) >|= fun r ->
-     Unix.sleep 100;
-     r)
+  Lwt_main.run (
+    let fd, close = match output with
+      | None -> Unix.stdout, fun () -> ()
+      | Some fn ->
+        let fd = Unix.openfile fn [ Unix.O_WRONLY ] 0o644 in
+        fd, fun () -> Unix.close fd
+    in
+    let reply () data =
+      let bytes = Bytes.of_string data in
+      let blen = String.length data in
+      let written = Unix.write fd bytes 0 blen in
+      if written <> blen then
+        Printf.printf "couldn't fully write (%d of %d bytes)" written blen;
+      Lwt.return_unit
+    in
+    (Http_lwt_client.request ?config ~meth ~headers ?body ~follow_redirect:(not no_follow) uri reply () >|= function
+      | Ok (resp, ()) ->
+        Format.fprintf Format.std_formatter "\n%a\n%!"
+          Http_lwt_client.pp_response resp;
+        Ok ()
+      | Error `Msg msg as e ->
+        Logs.err (fun m -> m "error %s" msg);
+        e) >|= fun r ->
+    close ();
+    r)
 
 let setup_log style_renderer level =
   Fmt_tty.setup_std_outputs ?style_renderer ();
diff --git a/src/http_lwt_client.ml b/src/http_lwt_client.ml
index 0922205..29b14cf 100644
--- a/src/http_lwt_client.ml
+++ b/src/http_lwt_client.ml
@@ -71,9 +71,9 @@ let prep_http_1_1_headers headers host user_pass blen =
   let headers = add headers "user-agent" ("http-lwt-client/%%VERSION_NUM%%") in
   let headers = add headers "host" host in
   let headers = add headers "connection" "close" in
-  let headers = match blen with
-    | None -> headers
-    | Some x -> add headers "content-length" (string_of_int x)
+  let headers =
+    add headers "content-length"
+      (string_of_int (Option.value ~default:0 blen))
   in
   add_authentication ~add headers user_pass
 
@@ -82,7 +82,8 @@ let prep_h2_headers headers host user_pass blen =
   let add hdr = H2.Headers.add_unless_exists hdr ?sensitive:None in
   let headers = add headers ":authority" host in
   let headers =
-    add headers "content-length" (string_of_int (Option.value ~default:0 blen))
+    add headers "content-length"
+      (string_of_int (Option.value ~default:0 blen))
   in
   add_authentication ~add headers user_pass
 
@@ -100,8 +101,8 @@ let pp_response ppf { version ; status ; reason ; headers } =
   Format.fprintf ppf "((version \"%a\") (status %a) (reason %S) (headers %a))"
     Version.pp_hum version Status.pp_hum status reason Headers.pp_hum headers
 
-let single_http_1_1_request ?config fd user_pass host meth path headers body =
-  let blen = match body with None -> None | Some x -> Some (String.length x) in
+let single_http_1_1_request ?config fd user_pass host meth path headers body f f_init =
+  let blen = Option.map String.length body in
   let headers = prep_http_1_1_headers headers host user_pass blen in
   let req = Httpaf.Request.create ~headers meth path in
   let finished, notify_finished = Lwt.wait () in
@@ -126,15 +127,20 @@ let single_http_1_1_request ?config fd user_pass host meth path headers body =
     wakeup (Ok (response, data))
   in
   let response_handler response response_body =
+    let open Lwt.Infix in
     let rec on_read on_eof data bs ~off ~len =
-      let data = data ^ Bigstringaf.substring ~off ~len bs in
+      let data =
+        data >>= fun data ->
+        f data (Bigstringaf.substring ~off ~len bs)
+      in
       Httpaf.Body.schedule_read response_body
         ~on_read:(on_read on_eof data)
-        ~on_eof:(on_eof response (Some data))
+        ~on_eof:(on_eof response data)
     in
+    let f_init = Lwt.return f_init in
     Httpaf.Body.schedule_read response_body
-      ~on_read:(on_read on_eof "")
-      ~on_eof:(on_eof response None)
+      ~on_read:(on_read on_eof f_init)
+      ~on_eof:(on_eof response f_init)
   in
   let error_handler e =
     let err = match e with
@@ -158,8 +164,8 @@ let single_http_1_1_request ?config fd user_pass host meth path headers body =
   Httpaf.Body.close_writer request_body;
   finished
 
-let single_h2_request ?config fd scheme user_pass host meth path headers body =
-  let blen = match body with None -> None | Some x -> Some (String.length x) in
+let single_h2_request ?config fd scheme user_pass host meth path headers body f f_init =
+  let blen = Option.map String.length body in
   let headers = prep_h2_headers headers host user_pass blen in
   let req = H2.Request.create ~scheme ~headers meth path in
   Logs.debug (fun m -> m "Sending @[<v 0>%a@]" H2.Request.pp_hum req);
@@ -182,15 +188,20 @@ let single_h2_request ?config fd scheme user_pass host meth path headers body =
     wakeup (Ok (response, data))
   in
   let response_handler response response_body =
+    let open Lwt.Infix in
     let rec on_read on_eof data bs ~off ~len =
-      let data = data ^ Bigstringaf.substring ~off ~len bs in
+      let data =
+        data >>= fun data ->
+        f data (Bigstringaf.substring ~off ~len bs)
+      in
       H2.Body.Reader.schedule_read response_body
         ~on_read:(on_read on_eof data)
-        ~on_eof:(on_eof response (Some data))
+        ~on_eof:(on_eof response data)
     in
+    let f_init = Lwt.return f_init in
     H2.Body.Reader.schedule_read response_body
-      ~on_read:(on_read on_eof "")
-      ~on_eof:(on_eof response None)
+      ~on_read:(on_read on_eof f_init)
+      ~on_eof:(on_eof response f_init)
   in
   let error_handler e =
     let err = match e with
@@ -233,7 +244,7 @@ let alpn_protocol = function
       None
     | Error () -> None
 
-let single_request resolver ?config tls_config ~meth ~headers ?body uri =
+let single_request resolver ?config tls_config ~meth ~headers ?body uri f f_init =
   Lwt_result.lift (decode_uri uri) >>= fun (tls, scheme, user_pass, host, port, path) ->
   (if tls then
      Lwt_result.lift (Lazy.force tls_config) >|= function
@@ -245,25 +256,27 @@ let single_request resolver ?config tls_config ~meth ~headers ?body uri =
    else
      Lwt_result.return None) >>= fun tls_config ->
   connect resolver ?port ?tls_config host >>= fun fd ->
-  match alpn_protocol fd, config with
+  begin match alpn_protocol fd, config with
   | (Some `HTTP_1_1 | None), Some (`HTTP_1_1 config) ->
     Logs.debug (fun m -> m "Start an http/1.1 connection as expected.");
-    single_http_1_1_request ~config fd user_pass host meth path headers body
+    single_http_1_1_request ~config fd user_pass host meth path headers body f f_init
   | (Some `HTTP_1_1 | None), None ->
     Logs.debug (fun m -> m "Start an http/1.1 connection by default.");
-    single_http_1_1_request fd user_pass host meth path headers body
+    single_http_1_1_request fd user_pass host meth path headers body f f_init
   | (Some `H2 | None), Some (`H2 config) ->
     Logs.debug (fun m -> m "Start an h2 connection as expected.");
-    single_h2_request ~config fd scheme user_pass host meth path headers body
+    single_h2_request ~config fd scheme user_pass host meth path headers body f f_init
   | Some `H2, None ->
     Logs.debug (fun m -> m "Start an h2 connection as requested by the server.");
-    single_h2_request fd scheme user_pass host meth path headers body
+    single_h2_request fd scheme user_pass host meth path headers body f f_init
   | Some `H2, Some (`HTTP_1_1 _config) ->
     Logs.warn (fun m -> m "Initiate an h2 connection despite a requested http/1.1 connection.");
-    single_h2_request fd scheme user_pass host meth path headers body
+    single_h2_request fd scheme user_pass host meth path headers body f f_init
   | Some `HTTP_1_1, Some (`H2 _config) ->
     Logs.warn (fun m -> m "Initiate an http/1.1 connection despite a requested h2 connection.");
-    single_http_1_1_request fd user_pass host meth path headers body
+    single_http_1_1_request fd user_pass host meth path headers body f f_init
+  end >>= fun (resp, body) ->
+  Lwt.map (fun body -> Ok (resp, body)) body
 
 let resolve_location ~uri ~location =
   match String.split_on_char '/' location with
@@ -281,7 +294,7 @@ let resolve_location ~uri ~location =
 
 let default_auth = lazy (Ca_certs.authenticator ())
 
-let one_request
+let request
     ?config
     ?tls_config
     ?authenticator
@@ -292,6 +305,7 @@ let one_request
     ?(follow_redirect = true)
     ?(happy_eyeballs = Happy_eyeballs_lwt.create ())
     uri
+    f f_init
   =
   let tls_config : ([`Custom of Tls.Config.client | `Default of Tls.Config.client ], [> `Msg of string ]) result Lazy.t =
     lazy
@@ -312,13 +326,13 @@ let one_request
            auth)
   in
   if not follow_redirect then
-    single_request happy_eyeballs ?config tls_config ~meth ~headers ?body uri
+    single_request happy_eyeballs ?config tls_config ~meth ~headers ?body uri f f_init
   else
     let rec follow_redirect count uri =
       if count = 0 then
         Lwt.return (Error (`Msg "redirect limit exceeded"))
       else
-        single_request happy_eyeballs ?config tls_config ~meth ~headers ?body uri
+        single_request happy_eyeballs ?config tls_config ~meth ~headers ?body uri f f_init
         >>= fun (resp, body) ->
         if Status.is_redirection resp.status then
           (match Headers.get resp.headers "location" with
diff --git a/src/http_lwt_client.mli b/src/http_lwt_client.mli
index 61a0140..f871509 100644
--- a/src/http_lwt_client.mli
+++ b/src/http_lwt_client.mli
@@ -33,11 +33,15 @@ type response =
 (** [pp_response ppf response] pretty-prints the [response] on [ppf]. *)
 val pp_response : Format.formatter -> response -> unit
 
-(** [one_request ~config ~authenticator ~meth ~headers ~body ~max_redirect
-    ~follow_redirect ~happy_eyeballs uri] does a single request of [uri] and
-    returns the response. By default, up to 5 redirects ([max_redirect]) are
-    followed. If [follow_redirect] is false, no redirect is followed (defaults
-    to true). The default HTTP request type ([meth]) is [GET].
+(** [request ~config ~authenticator ~meth ~headers ~body ~max_redirect
+    ~follow_redirect ~happy_eyeballs uri f init] does a single request of [uri]
+    and returns the response. Each time part of the body is received,
+    [f acc part] is called, with [acc] being the last return value of [f]
+    (or [init] if it is the first time) and [part] being the body part received.
+
+    By default, up to 5 redirects ([max_redirect]) are followed.
+    If [follow_redirect] is false, no redirect is followed (defaults to true).
+    The default HTTP request type ([meth]) is [GET].
 
     If no [tls_config] is provided, a default one is used, with alpn and
     authenticators. If a [tls_config] is provided, this is used unmodified.
@@ -53,7 +57,7 @@ val pp_response : Format.formatter -> response -> unit
     The [happy-eyeballs] opam package is used to establish the TCP connection,
     which prefers IPv6 over IPv4.
 *)
-val one_request
+val request
   : ?config : [ `HTTP_1_1 of Httpaf.Config.t | `H2 of H2.Config.t ]
   -> ?tls_config:Tls.Config.client
   -> ?authenticator:X509.Authenticator.t
@@ -64,4 +68,6 @@ val one_request
   -> ?follow_redirect:bool
   -> ?happy_eyeballs:Happy_eyeballs_lwt.t
   -> string
-  -> (response * string option, [> `Msg of string ]) Lwt_result.t
+  -> ('a -> string -> 'a Lwt.t)
+  -> 'a
+  -> (response * 'a, [> `Msg of string ]) Lwt_result.t