diff --git a/async/h2_async.ml b/async/h2_async.ml
index e372930..bbde4ca 100644
--- a/async/h2_async.ml
+++ b/async/h2_async.ml
@@ -132,9 +132,17 @@ module Client = struct
 
   let request t = Client_connection.request t.connection
   let ping t = Client_connection.ping t.connection
-  let shutdown t = Client_runtime.shutdown t.runtime
+
+  let shutdown t =
+    (* Do we need to shutdown the connection here? *)
+    Client_connection.shutdown t.connection;
+    Client_runtime.shutdown t.runtime
+
   let is_closed t = Client_runtime.is_closed t.runtime
 
+  (* Under no circumstances can this return an exception! *)
+  let close_finished t = Client_runtime.close_finished t.runtime
+
   module SSL = struct
     module Client_runtime = Gluten_async.Client.SSL
 
@@ -176,6 +184,10 @@ module Client = struct
     let ping t = Client_connection.ping t.connection
     let shutdown t = Client_runtime.shutdown t.runtime
     let is_closed t = Client_runtime.is_closed t.runtime
+
+    let close_finished t =
+      Client_runtime.close_finished t.runtime >>| fun () ->
+      H2.Client_connection.shutdown t.connection
   end
 
   module TLS = struct
@@ -223,5 +235,9 @@ module Client = struct
     let ping t = Client_connection.ping t.connection
     let shutdown t = Client_runtime.shutdown t.runtime
     let is_closed t = Client_runtime.is_closed t.runtime
+
+    let close_finished t =
+      Client_runtime.close_finished t.runtime >>| fun () ->
+      H2.Client_connection.shutdown t.connection
   end
 end
diff --git a/async/h2_async_intf.ml b/async/h2_async_intf.ml
index df949fe..7e8f804 100644
--- a/async/h2_async_intf.ml
+++ b/async/h2_async_intf.ml
@@ -80,4 +80,5 @@ module type Client = sig
 
   val shutdown : _ t -> unit Deferred.t
   val is_closed : _ t -> bool
+  val close_finished : _ t -> unit Deferred.t
 end