diff --git a/lib_eio_luv/tests/process.md b/lib_eio_luv/tests/process.md
index babec9efa..46aae4ac0 100644
--- a/lib_eio_luv/tests/process.md
+++ b/lib_eio_luv/tests/process.md
@@ -12,12 +12,11 @@ A helper function for reading all of the bytes from a handle.
 
 ```ocaml
 let read_all handle buf =
-    let rec read acc =
-      try 
-        let i = Eio_luv.Low_level.Stream.read_into handle buf in
-        read (acc + i)
-      with End_of_file -> acc
-    in read 0
+  let rec read acc =
+    match Eio_luv.Low_level.Stream.read_into handle buf with
+    | i -> read (acc + i)
+    | exception End_of_file -> acc
+  in read 0
 ```
 
 A simple `echo hello` process redirects to stdout.
@@ -42,7 +41,7 @@ Using a pipe to redirect output to a buffer.
   let parent_pipe = Eio_luv.Low_level.Pipe.init ~sw () in
   let buf = Luv.Buffer.create 32 in 
   let redirect = Eio_luv.Low_level.Process.[
-    to_parent_pipe ~fd:Luv.Process.stdout ~parent_pipe:parent_pipe ()
+    to_parent_pipe ~fd:Luv.Process.stdout ~parent_pipe ()
   ] in
   let t = Process.spawn ~sw ~redirect "echo" [ "echo"; "Hello,"; "World!" ] in
   let read = read_all parent_pipe buf in
@@ -88,17 +87,14 @@ Forgetting to wait for a process to finish stops the process.
 
 ```ocaml
 # Eio_luv.run @@ fun _env ->
-  let proc = ref None in
-  let run () =
+  let proc =
     Switch.run @@ fun sw ->
     let redirect = Luv.Process.[
       inherit_fd ~fd:stdout ~from_parent_fd:stdout ()
     ] in
-    let t = Process.spawn ~sw ~redirect "sleep" [ "sleep"; "10" ] in
-    proc := Some t
+    Process.spawn ~sw ~redirect "sleep" [ "sleep"; "10" ]
   in
-  run ();
-  Process.await_exit (Option.get !proc);;
+  Process.await_exit proc;;
 - : int * int64 = (9, 0L)
 ```
 
@@ -106,17 +102,15 @@ Stopping a process interacts nicely with switches.
 
 ```ocaml
 # Eio_luv.run @@ fun _env ->
-  let proc = ref None in
-  let run () =
+  let proc =
     Switch.run @@ fun sw ->
     let redirect = Luv.Process.[
       inherit_fd ~fd:stdout ~from_parent_fd:stdout ()
     ] in
     let t = Process.spawn ~sw ~redirect "sleep" [ "sleep"; "10" ] in
     Process.send_signal t Luv.Signal.sigkill;
-    proc := Some t
+    t
   in
-  run ();
-  Process.await_exit (Option.get !proc);;
+  Process.await_exit proc;;
 - : int * int64 = (9, 0L)
 ```