diff --git a/pkg/client/unversioned/remotecommand/v1.go b/pkg/client/unversioned/remotecommand/v1.go
index b10e5e1f1e7..f5428e0f953 100644
--- a/pkg/client/unversioned/remotecommand/v1.go
+++ b/pkg/client/unversioned/remotecommand/v1.go
@@ -55,12 +55,57 @@ func (e *streamProtocolV1) stream(conn httpstream.Connection) error {
 		}
 	}
 
+	var (
+		err                                                  error
+		errorStream, remoteStdin, remoteStdout, remoteStderr httpstream.Stream
+	)
+
+	// set up all the streams first
 	headers := http.Header{}
 	headers.Set(api.StreamType, api.StreamTypeError)
-	errorStream, err := conn.CreateStream(headers)
+	errorStream, err = conn.CreateStream(headers)
 	if err != nil {
 		return err
 	}
+	defer errorStream.Reset()
+
+	// Create all the streams first, then start the copy goroutines. The server doesn't start its copy
+	// goroutines until it's received all of the streams. If the client creates the stdin stream and
+	// immediately begins copying stdin data to the server, it's possible to overwhelm and wedge the
+	// spdy frame handler in the server so that it is full of unprocessed frames. The frames aren't
+	// getting processed because the server hasn't started its copying, and it won't do that until it
+	// gets all the streams. By creating all the streams first, we ensure that the server is ready to
+	// process data before the client starts sending any. See https://issues.k8s.io/16373 for more info.
+	if e.stdin != nil {
+		headers.Set(api.StreamType, api.StreamTypeStdin)
+		remoteStdin, err = conn.CreateStream(headers)
+		if err != nil {
+			return err
+		}
+		defer remoteStdin.Reset()
+	}
+
+	if e.stdout != nil {
+		headers.Set(api.StreamType, api.StreamTypeStdout)
+		remoteStdout, err = conn.CreateStream(headers)
+		if err != nil {
+			return err
+		}
+		defer remoteStdout.Reset()
+	}
+
+	if e.stderr != nil && !e.tty {
+		headers.Set(api.StreamType, api.StreamTypeStderr)
+		remoteStderr, err = conn.CreateStream(headers)
+		if err != nil {
+			return err
+		}
+		defer remoteStderr.Reset()
+	}
+
+	// now that all the streams have been created, proceed with reading & copying
+
+	// always read from errorStream
 	go func() {
 		message, err := ioutil.ReadAll(errorStream)
 		if err != nil && err != io.EOF {
@@ -72,15 +117,8 @@ func (e *streamProtocolV1) stream(conn httpstream.Connection) error {
 			return
 		}
 	}()
-	defer errorStream.Reset()
 
 	if e.stdin != nil {
-		headers.Set(api.StreamType, api.StreamTypeStdin)
-		remoteStdin, err := conn.CreateStream(headers)
-		if err != nil {
-			return err
-		}
-		defer remoteStdin.Reset()
 		// TODO this goroutine will never exit cleanly (the io.Copy never unblocks)
 		// because stdin is not closed until the process exits. If we try to call
 		// stdin.Close(), it returns no error but doesn't unblock the copy. It will
@@ -93,23 +131,11 @@ func (e *streamProtocolV1) stream(conn httpstream.Connection) error {
 
 	if e.stdout != nil {
 		waitCount++
-		headers.Set(api.StreamType, api.StreamTypeStdout)
-		remoteStdout, err := conn.CreateStream(headers)
-		if err != nil {
-			return err
-		}
-		defer remoteStdout.Reset()
 		go cp(api.StreamTypeStdout, e.stdout, remoteStdout)
 	}
 
 	if e.stderr != nil && !e.tty {
 		waitCount++
-		headers.Set(api.StreamType, api.StreamTypeStderr)
-		remoteStderr, err := conn.CreateStream(headers)
-		if err != nil {
-			return err
-		}
-		defer remoteStderr.Reset()
 		go cp(api.StreamTypeStderr, e.stderr, remoteStderr)
 	}
 
diff --git a/pkg/client/unversioned/remotecommand/v2.go b/pkg/client/unversioned/remotecommand/v2.go
index ca10dda4956..16ae32fab6b 100644
--- a/pkg/client/unversioned/remotecommand/v2.go
+++ b/pkg/client/unversioned/remotecommand/v2.go
@@ -42,16 +42,52 @@ type streamProtocolV2 struct {
 var _ streamProtocolHandler = &streamProtocolV2{}
 
 func (e *streamProtocolV2) stream(conn httpstream.Connection) error {
+	var (
+		err                                                  error
+		errorStream, remoteStdin, remoteStdout, remoteStderr httpstream.Stream
+	)
+
 	headers := http.Header{}
 
+	// set up all the streams first
 	// set up error stream
 	errorChan := make(chan error)
 	headers.Set(api.StreamType, api.StreamTypeError)
-	errorStream, err := conn.CreateStream(headers)
+	errorStream, err = conn.CreateStream(headers)
 	if err != nil {
 		return err
 	}
 
+	// set up stdin stream
+	if e.stdin != nil {
+		headers.Set(api.StreamType, api.StreamTypeStdin)
+		remoteStdin, err = conn.CreateStream(headers)
+		if err != nil {
+			return err
+		}
+	}
+
+	// set up stdout stream
+	if e.stdout != nil {
+		headers.Set(api.StreamType, api.StreamTypeStdout)
+		remoteStdout, err = conn.CreateStream(headers)
+		if err != nil {
+			return err
+		}
+	}
+
+	// set up stderr stream
+	if e.stderr != nil && !e.tty {
+		headers.Set(api.StreamType, api.StreamTypeStderr)
+		remoteStderr, err = conn.CreateStream(headers)
+		if err != nil {
+			return err
+		}
+	}
+
+	// now that all the streams have been created, proceed with reading & copying
+
+	// always read from errorStream
 	go func() {
 		message, err := ioutil.ReadAll(errorStream)
 		switch {
@@ -68,14 +104,7 @@ func (e *streamProtocolV2) stream(conn httpstream.Connection) error {
 	var wg sync.WaitGroup
 	var once sync.Once
 
-	// set up stdin stream
 	if e.stdin != nil {
-		headers.Set(api.StreamType, api.StreamTypeStdin)
-		remoteStdin, err := conn.CreateStream(headers)
-		if err != nil {
-			return err
-		}
-
 		// copy from client's stdin to container's stdin
 		go func() {
 			// if e.stdin is noninteractive, e.g. `echo abc | kubectl exec -i <pod> -- cat`, make sure
@@ -109,14 +138,7 @@ func (e *streamProtocolV2) stream(conn httpstream.Connection) error {
 		}()
 	}
 
-	// set up stdout stream
 	if e.stdout != nil {
-		headers.Set(api.StreamType, api.StreamTypeStdout)
-		remoteStdout, err := conn.CreateStream(headers)
-		if err != nil {
-			return err
-		}
-
 		wg.Add(1)
 		go func() {
 			defer wg.Done()
@@ -126,14 +148,7 @@ func (e *streamProtocolV2) stream(conn httpstream.Connection) error {
 		}()
 	}
 
-	// set up stderr stream
 	if e.stderr != nil && !e.tty {
-		headers.Set(api.StreamType, api.StreamTypeStderr)
-		remoteStderr, err := conn.CreateStream(headers)
-		if err != nil {
-			return err
-		}
-
 		wg.Add(1)
 		go func() {
 			defer wg.Done()