diff --git a/jupyterhub/spawner.py b/jupyterhub/spawner.py
index 137e6f78..274e407b 100644
--- a/jupyterhub/spawner.py
+++ b/jupyterhub/spawner.py
@@ -252,7 +252,7 @@ class Spawner(LoggingConfigurable):
             if status is not None:
                 break
             else:
-                yield gen.Task(loop.add_timeout, loop.time() + self.death_interval)
+                yield gen.sleep(self.death_interval)
 
 def _try_setcwd(path):
     """Try to set CWD, walking up and ultimately falling back to a temp dir"""
diff --git a/jupyterhub/tests/mocking.py b/jupyterhub/tests/mocking.py
index bec40c7c..43411483 100644
--- a/jupyterhub/tests/mocking.py
+++ b/jupyterhub/tests/mocking.py
@@ -53,12 +53,12 @@ class SlowSpawner(MockSpawner):
     
     @gen.coroutine
     def start(self):
-        yield gen.Task(IOLoop.current().add_timeout, timedelta(seconds=2))
+        yield gen.sleep(2)
         yield super().start()
     
     @gen.coroutine
     def stop(self):
-        yield gen.Task(IOLoop.current().add_timeout, timedelta(seconds=2))
+        yield gen.sleep(2)
         yield super().stop()
 
 
diff --git a/jupyterhub/tests/test_api.py b/jupyterhub/tests/test_api.py
index dc7facdf..117b5644 100644
--- a/jupyterhub/tests/test_api.py
+++ b/jupyterhub/tests/test_api.py
@@ -363,11 +363,10 @@ def test_slow_spawn(app, io_loop):
     assert app_user.spawn_pending
     assert not app_user.stop_pending
     
-    dt = timedelta(seconds=0.1)
     @gen.coroutine
     def wait_spawn():
         while app_user.spawn_pending:
-            yield gen.Task(io_loop.add_timeout, dt)
+            yield gen.sleep(0.1)
     
     io_loop.run_sync(wait_spawn)
     assert not app_user.spawn_pending
@@ -377,7 +376,7 @@ def test_slow_spawn(app, io_loop):
     @gen.coroutine
     def wait_stop():
         while app_user.stop_pending:
-            yield gen.Task(io_loop.add_timeout, dt)
+            yield gen.sleep(0.1)
 
     r = api_request(app, 'users', name, 'server', method='delete')
     r.raise_for_status()
@@ -410,11 +409,10 @@ def test_never_spawn(app, io_loop):
     assert app_user.spawner is not None
     assert app_user.spawn_pending
     
-    dt = timedelta(seconds=0.1)
     @gen.coroutine
     def wait_pending():
         while app_user.spawn_pending:
-            yield gen.Task(io_loop.add_timeout, dt)
+            yield gen.sleep(0.1)
     
     io_loop.run_sync(wait_pending)
     assert not app_user.spawn_pending
diff --git a/jupyterhub/utils.py b/jupyterhub/utils.py
index 8688f538..e9f8223d 100644
--- a/jupyterhub/utils.py
+++ b/jupyterhub/utils.py
@@ -41,7 +41,7 @@ def wait_for_server(ip, port, timeout=10):
                 app_log.error("Unexpected error waiting for %s:%i %s",
                     ip, port, e
                 )
-            yield gen.Task(loop.add_timeout, loop.time() + 0.1)
+            yield gen.sleep(0.1)
         else:
             return
     raise TimeoutError("Server at {ip}:{port} didn't respond in {timeout} seconds".format(
@@ -67,14 +67,14 @@ def wait_for_http_server(url, timeout=10):
                     # we expect 599 for no connection,
                     # but 502 or other proxy error is conceivable
                     app_log.warn("Server at %s responded with error: %s", url, e.code)
-                yield gen.Task(loop.add_timeout, loop.time() + 0.25)
+                yield gen.sleep(0.1)
             else:
                 app_log.debug("Server at %s responded with %s", url, e.code)
                 return
         except (OSError, socket.error) as e:
             if e.errno not in {errno.ECONNABORTED, errno.ECONNREFUSED, errno.ECONNRESET}:
                 app_log.warn("Failed to connect to %s (%s)", url, e)
-            yield gen.Task(loop.add_timeout, loop.time() + 0.25)
+            yield gen.sleep(0.1)
         else:
             return
     
diff --git a/requirements.txt b/requirements.txt
index ca60a120..9946e3d3 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,5 @@
 traitlets>=4
-tornado>=4
+tornado>=4.1
 jinja2
 pamela
 sqlalchemy