diff --git a/lib/mint/http2.ex b/lib/mint/http2.ex
index df54869f..6642f25b 100644
--- a/lib/mint/http2.ex
+++ b/lib/mint/http2.ex
@@ -1566,7 +1566,7 @@ defmodule Mint.HTTP2 do
         responses = [{:data, stream.ref, data} | responses]
 
         if flag_set?(flags, :data, :end_stream) do
-          conn = close_stream!(conn, stream.id, :no_error)
+          conn = close_stream!(conn, stream.id, :remote_end_stream)
           {conn, [{:done, stream.ref} | responses]}
         else
           {conn, responses}
@@ -1675,7 +1675,7 @@ defmodule Mint.HTTP2 do
                 {conn, responses}
 
               end_stream? ->
-                conn = close_stream!(conn, stream.id, :no_error)
+                conn = close_stream!(conn, stream.id, :remote_end_stream)
                 {conn, [{:done, ref} | new_responses]}
 
               true ->
@@ -1685,7 +1685,7 @@ defmodule Mint.HTTP2 do
             end
 
           end_stream? ->
-            conn = close_stream!(conn, stream.id, :no_error)
+            conn = close_stream!(conn, stream.id, :remote_end_stream)
             {conn, [{:done, ref} | new_responses]}
 
           true ->
@@ -1695,7 +1695,7 @@ defmodule Mint.HTTP2 do
       # Trailer headers. We don't care about the :status header here.
       headers when received_first_headers? ->
         if end_stream? do
-          conn = close_stream!(conn, stream.id, :no_error)
+          conn = close_stream!(conn, stream.id, :remote_end_stream)
           headers = headers |> Headers.remove_unallowed_trailer() |> join_cookie_headers()
           {conn, [{:done, ref}, {:headers, ref, headers} | responses]}
         else
@@ -2094,18 +2094,27 @@ defmodule Mint.HTTP2 do
     throw({:mint, %{conn | state: :closed}, wrap_error({error_code, debug_data})})
   end
 
-  defp close_stream!(conn, stream_id, error_code) do
+  # Reason is either an error code or `remote_end_stream`
+  defp close_stream!(conn, stream_id, reason) do
     stream = Map.fetch!(conn.streams, stream_id)
 
-    # First of all we send a RST_STREAM with the given error code so that we
-    # move the stream to the :closed state (that is, we remove it).
-    rst_stream_frame = rst_stream(stream_id: stream_id, error_code: error_code)
-
     conn =
-      if open?(conn) do
-        send!(conn, Frame.encode(rst_stream_frame))
-      else
-        conn
+      cond do
+        # If the stream is ended on both sides, it is already deemed closed and
+        # there's no need to send a RST_STREAM frame
+        reason == :remote_end_stream and stream.state == :half_closed_local ->
+          conn
+
+        # We send a RST_STREAM with the given error code so that we move the
+        # stream to the :closed state (that is, we remove it).
+        open?(conn) ->
+          error_code = if reason == :remote_end_stream, do: :no_error, else: reason
+          rst_stream_frame = rst_stream(stream_id: stream_id, error_code: error_code)
+          send!(conn, Frame.encode(rst_stream_frame))
+
+        # If the connection is already closed, no-op
+        true ->
+          conn
       end
 
     delete_stream(conn, stream)
diff --git a/test/mint/http2/conn_test.exs b/test/mint/http2/conn_test.exs
index 429d3000..41bcd4d3 100644
--- a/test/mint/http2/conn_test.exs
+++ b/test/mint/http2/conn_test.exs
@@ -325,7 +325,7 @@ defmodule Mint.HTTP2Test do
 
       assert [{:status, ^ref, 200}, {:headers, ^ref, []}, {:done, ^ref}] = responses
 
-      assert_recv_frames [rst_stream(stream_id: ^stream_id)]
+      assert Enum.empty?(conn.streams)
 
       assert {:ok, %HTTP2{} = conn, []} =
                stream_frames(conn, [
@@ -335,6 +335,25 @@ defmodule Mint.HTTP2Test do
 
       assert HTTP2.open?(conn)
     end
+
+    test "doesn't send RST_STREAM when stream is declared ended in both sides", %{conn: conn} do
+      {conn, ref} = open_request(conn)
+
+      assert_recv_frames [headers(stream_id: stream_id)]
+
+      assert conn.streams[stream_id].state == :half_closed_local
+
+      assert {:ok, %HTTP2{} = conn, responses} =
+               stream_frames(conn, [
+                 {:headers, stream_id, [{":status", "200"}], [:end_headers, :end_stream]}
+               ])
+
+      assert [{:status, ^ref, 200}, {:headers, ^ref, []}, {:done, ^ref}] = responses
+
+      assert_recv_frames([])
+      assert is_nil(conn.streams[stream_id])
+      assert HTTP2.open?(conn)
+    end
   end
 
   describe "stream state transitions" do
@@ -763,8 +782,7 @@ defmodule Mint.HTTP2Test do
 
       assert [{:status, ^ref, 200}, {:headers, ^ref, _headers}, {:done, ^ref}] = responses
 
-      assert_recv_frames [rst_stream(error_code: :no_error)]
-
+      assert Enum.empty?(conn.streams)
       assert HTTP2.open?(conn)
     end
 
@@ -1466,8 +1484,6 @@ defmodule Mint.HTTP2Test do
                {:done, ^ref}
              ] = responses
 
-      assert_recv_frames [rst_stream(stream_id: ^stream_id, error_code: :no_error)]
-
       # Here we send headers for the two promised streams. Note that neither of the
       # header frames have the END_STREAM flag set otherwise we close the streams and
       # they don't count towards the open stream count.