diff --git a/api/client/hijack.go b/api/client/hijack.go
index 14e3bc58f7..0cc57a2e74 100644
--- a/api/client/hijack.go
+++ b/api/client/hijack.go
@@ -16,7 +16,6 @@ import (
 	"github.com/Sirupsen/logrus"
 	"github.com/docker/docker/api"
 	"github.com/docker/docker/autogen/dockerversion"
-	"github.com/docker/docker/pkg/promise"
 	"github.com/docker/docker/pkg/stdcopy"
 	"github.com/docker/docker/pkg/term"
 )
@@ -186,8 +185,6 @@ func (cli *DockerCli) hijack(method, path string, setRawTerminal bool, in io.Rea
 		started <- rwc
 	}
 
-	var receiveStdout chan error
-
 	var oldState *term.State
 
 	if in != nil && setRawTerminal && cli.isTerminalIn && os.Getenv("NORAW") == "" {
@@ -198,19 +195,15 @@ func (cli *DockerCli) hijack(method, path string, setRawTerminal bool, in io.Rea
 		defer term.RestoreTerminal(cli.inFd, oldState)
 	}
 
+	receiveStdout := make(chan error, 1)
 	if stdout != nil || stderr != nil {
-		receiveStdout = promise.Go(func() (err error) {
+		go func() {
 			defer func() {
 				if in != nil {
 					if setRawTerminal && cli.isTerminalIn {
 						term.RestoreTerminal(cli.inFd, oldState)
 					}
-					// For some reason this Close call blocks on darwin..
-					// As the client exists right after, simply discard the close
-					// until we find a better solution.
-					if runtime.GOOS != "darwin" {
-						in.Close()
-					}
+					in.Close()
 				}
 			}()
 
@@ -221,11 +214,12 @@ func (cli *DockerCli) hijack(method, path string, setRawTerminal bool, in io.Rea
 				_, err = stdcopy.StdCopy(stdout, stderr, br)
 			}
 			logrus.Debugf("[hijack] End of stdout")
-			return err
-		})
+			receiveStdout <- err
+		}()
 	}
 
-	sendStdin := promise.Go(func() error {
+	stdinDone := make(chan struct{})
+	go func() {
 		if in != nil {
 			io.Copy(rwc, in)
 			logrus.Debugf("[hijack] End of stdin")
@@ -238,22 +232,24 @@ func (cli *DockerCli) hijack(method, path string, setRawTerminal bool, in io.Rea
 				logrus.Debugf("Couldn't send EOF: %s", err)
 			}
 		}
-		// Discard errors due to pipe interruption
-		return nil
-	})
+		close(stdinDone)
+	}()
 
-	if stdout != nil || stderr != nil {
-		if err := <-receiveStdout; err != nil {
+	select {
+	case err := <-receiveStdout:
+		if err != nil {
 			logrus.Debugf("Error receiveStdout: %s", err)
-			return err
+		}
+		if cli.isTerminalIn {
+			return nil
+		}
+	case <-stdinDone:
+		if stdout != nil || stderr != nil {
+			if err := <-receiveStdout; err != nil {
+				logrus.Debugf("Error receiveStdout: %s", err)
+			}
 		}
 	}
 
-	if !cli.isTerminalIn {
-		if err := <-sendStdin; err != nil {
-			logrus.Debugf("Error sendStdin: %s", err)
-			return err
-		}
-	}
 	return nil
 }
diff --git a/integration-cli/docker_cli_run_test.go b/integration-cli/docker_cli_run_test.go
index f6485c2dec..f6fb99b46c 100644
--- a/integration-cli/docker_cli_run_test.go
+++ b/integration-cli/docker_cli_run_test.go
@@ -3384,3 +3384,24 @@ func (s *DockerSuite) TestTwoContainersInNetHost(c *check.C) {
 	dockerCmd(c, "stop", "first")
 	dockerCmd(c, "stop", "second")
 }
+
+// #11957 - stdin with no tty does not exit if stdin is not closed even though container exited
+func (s *DockerSuite) TestRunStdinBlockedAfterContainerExit(c *check.C) {
+	cmd := exec.Command(dockerBinary, "run", "-i", "--name=test", "busybox", "true")
+	in, err := cmd.StdinPipe()
+	c.Assert(err, check.IsNil)
+	defer in.Close()
+	c.Assert(cmd.Start(), check.IsNil)
+
+	waitChan := make(chan error)
+	go func() {
+		waitChan <- cmd.Wait()
+	}()
+
+	select {
+	case err := <-waitChan:
+		c.Assert(err, check.IsNil)
+	case <-time.After(3 * time.Second):
+		c.Fatal("timeout waiting for command to exit")
+	}
+}