diff --git a/bench/bench_copy.ml b/bench/bench_copy.ml
index 0249bf6e8..34d918aeb 100644
--- a/bench/bench_copy.ml
+++ b/bench/bench_copy.ml
@@ -6,6 +6,22 @@ let chunk_size = 1 lsl 16
 let n_chunks = 10000
 let n_bytes = n_chunks * chunk_size
 
+let rec await pid =
+  match Unix.waitpid [] pid with
+  | (_pid, status) -> status
+  | exception Unix.Unix_error (Unix.EINTR, _, _) -> await pid
+
+let run prog args =
+  await (Unix.create_process prog (Array.of_list (prog :: args)) Unix.stdin Unix.stdout Unix.stderr)
+
+let check_status = function
+  | Unix.WEXITED 0 -> ()
+  | _ -> assert false
+
+let generate_file name =
+  run "fallocate" [ "-l"; string_of_int n_bytes; name ]
+  |> check_status
+
 let run_client sock =
   Fiber.both
     (fun () ->
@@ -35,8 +51,26 @@ let time name service =
   traceln "%s: %.2f MB/s" name (bytes_per_second /. 1024. /. 1024.);
   Metric.create name (`Float bytes_per_second) "bytes/s" (name ^ " Flow.copy")
 
-let run _env =
+let time_fs fs name service =
+  let ( / ) = Eio.Path.(/) in
+  let fname_in = "cptest.in" in
+  let fname_out ="cptest.out" in
+  if not (Sys.file_exists fname_in) then generate_file fname_in;
+  Eio.Path.with_open_in (fs / fname_in) @@ fun inflow ->
+  Eio.Path.with_open_out ~create:(`Exclusive 0o644) (fs / fname_out) @@ fun outflow ->
+  let t0 = Unix.gettimeofday () in
+  service inflow outflow;
+  let t1 = Unix.gettimeofday () in
+  let time = t1 -. t0 in
+  let bytes_per_second = float n_bytes /. time in
+  traceln "%s: %.2f MB/s" name (bytes_per_second /. 1024. /. 1024.);
+  at_exit (fun () -> try Sys.remove fname_in with _ -> ());
+  Sys.remove fname_out;
+  Metric.create name (`Float bytes_per_second) "bytes/s" (name ^ " Flow.copy")
+
+let run env =
   [
+    time_fs env#fs "default_fs" (fun inflow outflow -> Eio.Flow.copy inflow outflow);
     time "default" (fun sock -> Eio.Flow.copy sock sock);
     time "buf_read" (fun sock ->
         let r = Eio.Buf_read.of_flow sock ~initial_size:(64 * 1024) ~max_size:(64 * 1024) |> Eio.Buf_read.as_flow in
diff --git a/lib_eio_linux/flow.ml b/lib_eio_linux/flow.ml
index a280527ef..4b82cdc65 100644
--- a/lib_eio_linux/flow.ml
+++ b/lib_eio_linux/flow.ml
@@ -1,5 +1,32 @@
 open Eio.Std
 
+(* When copying between files of finite size (e.g. regular files and
+   block devices), we want to batch up read and write requests to
+   submit at one go *)
+let batch_copy src dst =
+  let read_then_write_chunk infd outfd file_offset =
+    let buf = Low_level.alloc_fixed_or_wait () in
+    let len = Uring.Region.length buf in
+    Low_level.read_exactly ~file_offset infd buf len;
+    Low_level.write ~file_offset outfd buf len;
+    Low_level.free_fixed buf
+  in
+  let copy_file infd outfd insize block_size =
+    let module Int63 = Optint.Int63 in
+    Switch.run @@ fun sw ->
+    let rec copy_block file_offset =
+      let remaining = Int63.(sub insize file_offset) in
+      if remaining <> Int63.zero then (
+        let len = Int63.to_int (min (Int63.of_int block_size) remaining) in
+        Fiber.fork ~sw (fun () -> read_then_write_chunk infd outfd file_offset);
+        copy_block Int63.(add file_offset (of_int len))
+      )
+    in
+    copy_block Int63.zero
+  in
+  let insize = (Low_level.fstat src).size in
+  copy_file src dst insize 4096
+
 (* When copying between a source with an FD and a sink with an FD, we can share the chunk
    and avoid copying. *)
 let fast_copy src dst =
@@ -13,14 +40,17 @@ let fast_copy src dst =
       done
     with End_of_file -> ()
   in
-  Low_level.with_chunk ~fallback @@ fun chunk ->
-  let chunk_size = Uring.Region.length chunk in
-  try
-    while true do
-      let got = Low_level.read_upto src chunk chunk_size in
-      Low_level.write dst chunk got
-    done
-  with End_of_file -> ()
+  match (Low_level.fstat src).kind with
+  | `Block_device | `Regular_file ->  batch_copy src dst
+  | _ ->
+    Low_level.with_chunk ~fallback @@ fun chunk ->
+    let chunk_size = Uring.Region.length chunk in
+    try
+      while true do
+        let got = Low_level.read_upto src chunk chunk_size in
+        Low_level.write dst chunk got
+      done
+    with End_of_file -> ()
 
 (* Try a fast copy using splice. If the FDs don't support that, switch to copying. *)
 let _fast_copy_try_splice src dst =
@@ -35,7 +65,7 @@ let _fast_copy_try_splice src dst =
 
 (* XXX workaround for issue #319, PR #327 *)
 let fast_copy_try_splice src dst = fast_copy src dst
-    
+
 let[@tail_mod_cons] rec list_take n = function
   | [] -> []
   | x :: xs ->