diff --git a/jupyter_client/tests/signalkernel.py b/jupyter_client/tests/signalkernel.py
index e26731ff8..52679f6d5 100644
--- a/jupyter_client/tests/signalkernel.py
+++ b/jupyter_client/tests/signalkernel.py
@@ -10,7 +10,6 @@
 from ipykernel.displayhook import ZMQDisplayHook
 from ipykernel.kernelapp import IPKernelApp
 from ipykernel.kernelbase import Kernel
-from tornado.web import gen
 
 
 class SignalTestKernel(Kernel):
@@ -28,10 +27,9 @@ def __init__(self, **kwargs):
         if os.environ.get("NO_SIGTERM_REPLY", None) == "1":
             signal.signal(signal.SIGTERM, signal.SIG_IGN)
 
-    @gen.coroutine
-    def shutdown_request(self, stream, ident, parent):
+    async def shutdown_request(self, stream, ident, parent):
         if os.environ.get("NO_SHUTDOWN_REPLY") != "1":
-            yield gen.maybe_future(super().shutdown_request(stream, ident, parent))
+            await super().shutdown_request(stream, ident, parent)
 
     def do_execute(
         self, code, silent, store_history=True, user_expressions=None, allow_stdin=False
diff --git a/jupyter_client/tests/test_kernelmanager.py b/jupyter_client/tests/test_kernelmanager.py
index fc56c5b1a..44e136cfd 100644
--- a/jupyter_client/tests/test_kernelmanager.py
+++ b/jupyter_client/tests/test_kernelmanager.py
@@ -11,8 +11,6 @@
 from subprocess import PIPE
 
 import pytest
-from async_generator import async_generator
-from async_generator import yield_
 from jupyter_core import paths
 from traitlets.config.loader import Config
 
@@ -135,11 +133,9 @@ def async_km_subclass(config):
 
 
 @pytest.fixture
-@async_generator  # This is only necessary while Python 3.5 is support afterwhich both it and
-# yield_() can be removed
 async def start_async_kernel():
     km, kc = await start_new_async_kernel(kernel_name="signaltest")
-    await yield_((km, kc))
+    yield km, kc
     kc.stop_channels()
     await km.shutdown_kernel()
     assert km.context.closed
@@ -166,6 +162,9 @@ class TestKernelManagerShutDownGracefully:
     @pytest.mark.skipif(sys.platform == "win32", reason="Windows doesn't support signals")
     @pytest.mark.parametrize(*parameters)
     def test_signal_kernel_subprocesses(self, name, install, expected):
+        # ipykernel doesn't support 3.6 and this test uses async shutdown_request
+        if expected == _ShutdownStatus.ShutdownRequest and sys.version_info < (3, 7):
+            pytest.skip()
         install()
         km, kc = start_new_kernel(kernel_name=name)
         assert km._shutdown_status == _ShutdownStatus.Unset
@@ -180,6 +179,9 @@ def test_signal_kernel_subprocesses(self, name, install, expected):
     @pytest.mark.skipif(sys.platform == "win32", reason="Windows doesn't support signals")
     @pytest.mark.parametrize(*parameters)
     async def test_async_signal_kernel_subprocesses(self, name, install, expected):
+        # ipykernel doesn't support 3.6 and this test uses async shutdown_request
+        if expected == _ShutdownStatus.ShutdownRequest and sys.version_info < (3, 7):
+            pytest.skip()
         install()
         km, kc = await start_new_async_kernel(kernel_name=name)
         assert km._shutdown_status == _ShutdownStatus.Unset
diff --git a/setup.py b/setup.py
index 6a5d6d43e..63f065b26 100644
--- a/setup.py
+++ b/setup.py
@@ -79,7 +79,6 @@ def run(self):
     python_requires='>=3.6.1',
     extras_require={
         'test': [
-            'async_generator',
             'ipykernel',
             'ipython',
             'jedi<0.18; python_version<="3.6"',