diff --git a/http2/server.go b/http2/server.go
index 8f1701914c..6f8e8b0d98 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -52,10 +52,11 @@ import (
 )
 
 const (
-	prefaceTimeout        = 10 * time.Second
-	firstSettingsTimeout  = 2 * time.Second // should be in-flight with preface anyway
-	handlerChunkWriteSize = 4 << 10
-	defaultMaxStreams     = 250 // TODO: make this 100 as the GFE seems to?
+	prefaceTimeout         = 10 * time.Second
+	firstSettingsTimeout   = 2 * time.Second // should be in-flight with preface anyway
+	handlerChunkWriteSize  = 4 << 10
+	defaultMaxStreams      = 250 // TODO: make this 100 as the GFE seems to?
+	maxQueuedControlFrames = 10000
 )
 
 var (
@@ -163,6 +164,15 @@ func (s *Server) maxConcurrentStreams() uint32 {
 	return defaultMaxStreams
 }
 
+// maxQueuedControlFrames is the maximum number of control frames like
+// SETTINGS, PING and RST_STREAM that will be queued for writing before
+// the connection is closed to prevent memory exhaustion attacks.
+func (s *Server) maxQueuedControlFrames() int {
+	// TODO: if anybody asks, add a Server field, and remember to define the
+	// behavior of negative values.
+	return maxQueuedControlFrames
+}
+
 type serverInternalState struct {
 	mu          sync.Mutex
 	activeConns map[*serverConn]struct{}
@@ -482,6 +492,7 @@ type serverConn struct {
 	sawFirstSettings            bool // got the initial SETTINGS frame after the preface
 	needToSendSettingsAck       bool
 	unackedSettings             int    // how many SETTINGS have we sent without ACKs?
+	queuedControlFrames         int    // control frames in the writeSched queue
 	clientMaxStreams            uint32 // SETTINGS_MAX_CONCURRENT_STREAMS from client (our PUSH_PROMISE limit)
 	advMaxStreams               uint32 // our SETTINGS_MAX_CONCURRENT_STREAMS advertised the client
 	curClientStreams            uint32 // number of open streams initiated by the client
@@ -870,6 +881,14 @@ func (sc *serverConn) serve() {
 			}
 		}
 
+		// If the peer is causing us to generate a lot of control frames,
+		// but not reading them from us, assume they are trying to make us
+		// run out of memory.
+		if sc.queuedControlFrames > sc.srv.maxQueuedControlFrames() {
+			sc.vlogf("http2: too many control frames in send queue, closing connection")
+			return
+		}
+
 		// Start the shutdown timer after sending a GOAWAY. When sending GOAWAY
 		// with no error code (graceful shutdown), don't start the timer until
 		// all open streams have been completed.
@@ -1069,6 +1088,14 @@ func (sc *serverConn) writeFrame(wr FrameWriteRequest) {
 	}
 
 	if !ignoreWrite {
+		if wr.isControl() {
+			sc.queuedControlFrames++
+			// For extra safety, detect wraparounds, which should not happen,
+			// and pull the plug.
+			if sc.queuedControlFrames < 0 {
+				sc.conn.Close()
+			}
+		}
 		sc.writeSched.Push(wr)
 	}
 	sc.scheduleFrameWrite()
@@ -1186,10 +1213,8 @@ func (sc *serverConn) wroteFrame(res frameWriteResult) {
 // If a frame is already being written, nothing happens. This will be called again
 // when the frame is done being written.
 //
-// If a frame isn't being written we need to send one, the best frame
-// to send is selected, preferring first things that aren't
-// stream-specific (e.g. ACKing settings), and then finding the
-// highest priority stream.
+// If a frame isn't being written and we need to send one, the best frame
+// to send is selected by writeSched.
 //
 // If a frame isn't being written and there's nothing else to send, we
 // flush the write buffer.
@@ -1217,6 +1242,9 @@ func (sc *serverConn) scheduleFrameWrite() {
 		}
 		if !sc.inGoAway || sc.goAwayCode == ErrCodeNo {
 			if wr, ok := sc.writeSched.Pop(); ok {
+				if wr.isControl() {
+					sc.queuedControlFrames--
+				}
 				sc.startFrameWrite(wr)
 				continue
 			}
@@ -1509,6 +1537,8 @@ func (sc *serverConn) processSettings(f *SettingsFrame) error {
 	if err := f.ForeachSetting(sc.processSetting); err != nil {
 		return err
 	}
+	// TODO: judging by RFC 7540, Section 6.5.3 each SETTINGS frame should be
+	// acknowledged individually, even if multiple are received before the ACK.
 	sc.needToSendSettingsAck = true
 	sc.scheduleFrameWrite()
 	return nil
diff --git a/http2/server_test.go b/http2/server_test.go
index cc8326f5c3..ad6a07b390 100644
--- a/http2/server_test.go
+++ b/http2/server_test.go
@@ -1160,6 +1160,32 @@ func TestServer_Ping(t *testing.T) {
 	}
 }
 
+func TestServer_MaxQueuedControlFrames(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping in short mode")
+	}
+
+	st := newServerTester(t, nil)
+	defer st.Close()
+	st.greet()
+
+	const extraPings = 500000 // enough to fill the TCP buffers
+
+	for i := 0; i < maxQueuedControlFrames+extraPings; i++ {
+		pingData := [8]byte{1, 2, 3, 4, 5, 6, 7, 8}
+		if err := st.fr.WritePing(false, pingData); err != nil {
+			if i == 0 {
+				t.Fatal(err)
+			}
+			// We expect the connection to get closed by the server when the TCP
+			// buffer fills up and the write queue reaches MaxQueuedControlFrames.
+			t.Logf("sent %d PING frames", i)
+			return
+		}
+	}
+	t.Errorf("unexpected success sending all PING frames")
+}
+
 func TestServer_RejectsLargeFrames(t *testing.T) {
 	if runtime.GOOS == "windows" {
 		t.Skip("see golang.org/issue/13434")
diff --git a/http2/writesched.go b/http2/writesched.go
index 4fe3073073..f24d2b1e7d 100644
--- a/http2/writesched.go
+++ b/http2/writesched.go
@@ -32,7 +32,7 @@ type WriteScheduler interface {
 
 	// Pop dequeues the next frame to write. Returns false if no frames can
 	// be written. Frames with a given wr.StreamID() are Pop'd in the same
-	// order they are Push'd.
+	// order they are Push'd. No frames should be discarded except by CloseStream.
 	Pop() (wr FrameWriteRequest, ok bool)
 }
 
@@ -76,6 +76,12 @@ func (wr FrameWriteRequest) StreamID() uint32 {
 	return wr.stream.id
 }
 
+// isControl reports whether wr is a control frame for MaxQueuedControlFrames
+// purposes. That includes non-stream frames and RST_STREAM frames.
+func (wr FrameWriteRequest) isControl() bool {
+	return wr.stream == nil
+}
+
 // DataSize returns the number of flow control bytes that must be consumed
 // to write this entire frame. This is 0 for non-DATA frames.
 func (wr FrameWriteRequest) DataSize() int {