diff --git a/Makefile b/Makefile
index 1609a376..371d2ff9 100644
--- a/Makefile
+++ b/Makefile
@@ -15,7 +15,7 @@ CT_OPTS += -ct_hooks gun_ct_hook [] # -boot start_sasl
 LOCAL_DEPS = public_key ssl
 
 DEPS = cowlib
-dep_cowlib = git https://github.com/ninenines/cowlib 2.13.0
+dep_cowlib = git https://github.com/Nordix/cowlib respect-remote-concurrency-limit
 
 DOC_DEPS = asciideck
 
diff --git a/rebar.config b/rebar.config
index e242d757..9f9b2ac5 100644
--- a/rebar.config
+++ b/rebar.config
@@ -1,4 +1,4 @@
 {deps, [
-{cowlib,".*",{git,"https://github.com/ninenines/cowlib","2.13.0"}}
+{cowlib,".*",{git,"https://github.com/Nordix/cowlib","respect-remote-concurrency-limit"}}
 ]}.
 {erl_opts, [debug_info,warn_export_vars,warn_shadow_vars,warn_obsolete_guard]}.
diff --git a/src/gun_http2.erl b/src/gun_http2.erl
index bfd2d31c..c789e5cf 100644
--- a/src/gun_http2.erl
+++ b/src/gun_http2.erl
@@ -990,7 +990,44 @@ headers(State, RealStreamRef=[StreamRef|_], ReplyTo, Method, _Host, _Port,
 			{[], CookieStore0, EvHandlerState0}
 	end.
 
-request(State0=#http2_state{socket=Socket, transport=Transport, opts=Opts,
+request(State=#http2_state{http2_machine=HTTP2Machine}, StreamRef, ReplyTo, Method, Host, Port,
+		Path, Headers, Body, InitialFlow, CookieStore, EvHandler, EvHandlerState)
+		when is_reference(StreamRef) ->
+
+	case cow_http2_machine:is_remote_concurrency_limit_reached(HTTP2Machine) of
+		true ->
+			ReplyTo ! {gun_error, self(), stream_ref(State, StreamRef),
+				{stream_error, too_many_streams,
+				'Maximum concurrency limit has been reached.'}},
+			{[], CookieStore, EvHandlerState};
+		false ->
+			request1(State, StreamRef, ReplyTo, Method, Host, Port,
+				Path, Headers, Body, InitialFlow, CookieStore,
+				EvHandler, EvHandlerState)
+	end;
+%% Tunneled request.
+request(State, RealStreamRef=[StreamRef|_], ReplyTo, Method, _Host, _Port,
+		Path, Headers, Body, InitialFlow, CookieStore0, EvHandler, EvHandlerState0) ->
+	case get_stream_by_ref(State, StreamRef) of
+		%% @todo We should send an error to the user if the stream isn't ready.
+		Stream=#stream{tunnel=#tunnel{protocol=Proto, protocol_state=ProtoState0, info=#{
+				origin_host := OriginHost, origin_port := OriginPort}}} ->
+			{Commands, CookieStore, EvHandlerState1} = Proto:request(ProtoState0, RealStreamRef,
+				ReplyTo, Method, OriginHost, OriginPort, Path, Headers, Body,
+				InitialFlow, CookieStore0, EvHandler, EvHandlerState0),
+			{ResCommands, EvHandlerState} = tunnel_commands(Commands,
+				Stream, State, EvHandler, EvHandlerState1),
+			{ResCommands, CookieStore, EvHandlerState};
+		#stream{tunnel=undefined} ->
+			ReplyTo ! {gun_error, self(), stream_ref(State, StreamRef), {badstate,
+				"The stream is not a tunnel."}},
+			{[], CookieStore0, EvHandlerState0};
+		error ->
+			error_stream_not_found(State, StreamRef, ReplyTo),
+			{[], CookieStore0, EvHandlerState0}
+	end.
+
+request1(State0=#http2_state{socket=Socket, transport=Transport, opts=Opts,
 		http2_machine=HTTP2Machine0}, StreamRef, ReplyTo, Method, Host, Port,
 		Path, Headers0, Body, InitialFlow0, CookieStore0, EvHandler, EvHandlerState0)
 		when is_reference(StreamRef) ->
@@ -1005,7 +1042,7 @@ request(State0=#http2_state{socket=Socket, transport=Transport, opts=Opts,
 	RequestEvent = #{
 		stream_ref => RealStreamRef,
 		reply_to => ReplyTo,
-		function => ?FUNCTION_NAME,
+		function => request,
 		method => Method,
 		authority => Authority,
 		path => Path,
@@ -1039,27 +1076,6 @@ request(State0=#http2_state{socket=Socket, transport=Transport, opts=Opts,
 			end;
 		Error={error, _} ->
 			{Error, CookieStore, EvHandlerState1}
-	end;
-%% Tunneled request.
-request(State, RealStreamRef=[StreamRef|_], ReplyTo, Method, _Host, _Port,
-		Path, Headers, Body, InitialFlow, CookieStore0, EvHandler, EvHandlerState0) ->
-	case get_stream_by_ref(State, StreamRef) of
-		%% @todo We should send an error to the user if the stream isn't ready.
-		Stream=#stream{tunnel=#tunnel{protocol=Proto, protocol_state=ProtoState0, info=#{
-				origin_host := OriginHost, origin_port := OriginPort}}} ->
-			{Commands, CookieStore, EvHandlerState1} = Proto:request(ProtoState0, RealStreamRef,
-				ReplyTo, Method, OriginHost, OriginPort, Path, Headers, Body,
-				InitialFlow, CookieStore0, EvHandler, EvHandlerState0),
-			{ResCommands, EvHandlerState} = tunnel_commands(Commands,
-				Stream, State, EvHandler, EvHandlerState1),
-			{ResCommands, CookieStore, EvHandlerState};
-		#stream{tunnel=undefined} ->
-			ReplyTo ! {gun_error, self(), stream_ref(State, StreamRef), {badstate,
-				"The stream is not a tunnel."}},
-			{[], CookieStore0, EvHandlerState0};
-		error ->
-			error_stream_not_found(State, StreamRef, ReplyTo),
-			{[], CookieStore0, EvHandlerState0}
 	end.
 
 initial_flow(infinity, #{flow := InitialFlow}) -> InitialFlow;
diff --git a/test/rfc7540_SUITE.erl b/test/rfc7540_SUITE.erl
index 79ae347e..93103576 100644
--- a/test/rfc7540_SUITE.erl
+++ b/test/rfc7540_SUITE.erl
@@ -377,6 +377,31 @@ lingering_data_counts_toward_connection_window(_) ->
 	timer:sleep(300),
 	gun:close(ConnPid).
 
+respect_max_concurrent_streams(_) ->
+	doc("The SETTINGS_MAX_CONCURRENT_STREAMS setting can be used to "
+		"restrict the number of concurrent streams. (RFC7540 5.1.2, RFC7540 6.5.2)"),
+	Ref = make_ref(),
+	Routes = [{'_', [{"/delayed", delayed_hello_h, 500}]}],
+	ProtoOpts = #{
+		env => #{dispatch => cowboy_router:compile(Routes)},
+		tcp => #{protocols => [http2]},
+		max_concurrent_streams => 1
+	},
+	[{ref, _}, {port, Port}] = gun_test:init_cowboy_tcp(Ref, ProtoOpts, []),
+	try
+		{ok, ConnPid} = gun:open("localhost", Port, #{protocols => [http2]}),
+		{ok, http2} = gun:await_up(ConnPid),
+		StreamRef1 = gun:get(ConnPid, "/delayed"),
+		StreamRef2 = gun:get(ConnPid, "/delayed"),
+		{error, {stream_error, Reason}} = gun:await(ConnPid, StreamRef2),
+		{stream_error, too_many_streams, _Human} = Reason,
+		{response, nofin, 200, _} = gun:await(ConnPid, StreamRef1),
+		{ok, _} = gun:await_body(ConnPid, StreamRef1),
+		gun:close(ConnPid)
+	after
+		cowboy:stop_listener(Ref)
+	end.
+
 headers_priority_flag(_) ->
 	doc("HEADERS frames may include a PRIORITY flag indicating "
 		"that stream dependency information is attached. (RFC7540 6.2)"),