diff --git a/dockerpty/pty.py b/dockerpty/pty.py
index 25cb788..969fbd8 100644
--- a/dockerpty/pty.py
+++ b/dockerpty/pty.py
@@ -137,7 +137,9 @@ def start(self, sockets=None, **kwargs):
         pumps = []
 
         if pty_stdin and self.interactive:
-            pumps.append(io.Pump(io.Stream(self.stdin), pty_stdin, wait_for_output=False))
+            # if stdin isn't a TTY then this is probably an SSH session
+            # so wait for the EOF to happen before considering the Pump closed.
+            pumps.append(io.Pump(io.Stream(self.stdin), pty_stdin, wait_for_output=not sys.stdin.isatty()))
 
         if pty_stdout:
             pumps.append(io.Pump(pty_stdout, io.Stream(self.stdout), propagate_close=False))
@@ -360,11 +362,13 @@ def resize(self, size=None):
     def _hijack_tty(self, pumps):
         with tty.Terminal(self.operation.stdin, raw=self.operation.israw()):
             self.resize()
-            while True:
+            keep_running = True
+            stdin_stream = self._get_stdin_pump(pumps)
+            while keep_running:
                 read_pumps = [p for p in pumps if not p.eof]
                 write_streams = [p.to_stream for p in pumps if p.to_stream.needs_write()]
 
-                read_ready, write_ready = io.select(read_pumps, write_streams, timeout=60)
+                read_ready, write_ready = io.select(read_pumps, write_streams, timeout=2)
                 try:
                     for write_stream in write_ready:
                         write_stream.do_write()
@@ -372,9 +376,29 @@ def _hijack_tty(self, pumps):
                     for pump in read_ready:
                         pump.flush()
 
-                    if all([p.is_done() for p in pumps]):
+                    if sys.stdin.isatty():
+                        if all([p.is_done() for p in pumps]):
+                            keep_running = False
+                    elif stdin_stream.is_done():
+                        # If stdin isn't a TTY, this is probably an SSH session.
+                        # The most common use case for an SSH session without a
+                        # TTY is SCP/SFTP; like, someone coping a file to a remote
+                        # server. Those file transfer clients mark the end of
+                        # the session by sending an empty packet, then waiting
+                        # for the TCP session to terminate, We need to break out
+                        # of this loop to return control to the calling application
+                        # so it can tear down the SCP/SFTP process running inside
+                        # the container.
+                        keep_running = False
                         break
 
                 except SSLError as e:
                     if 'The operation did not complete' not in e.strerror:
                         raise e
+
+    @staticmethod
+    def _get_stdin_pump(pumps):
+        """Find the Pump connected to stdin, and return it"""
+        for pump in pumps:
+            if pump.from_stream.fd.name == '<stdin>':
+                return pump