diff --git a/tests/test_client.py b/tests/test_client.py
index 7c4d422..e6fa5ab 100644
--- a/tests/test_client.py
+++ b/tests/test_client.py
@@ -34,18 +34,29 @@ def test_can_be_constructed_on_https():
     Client(api_url="https://example.com", api_key="foo")
 
 
+# On Python 3.8/3.9, pytest.mark.asyncio doesn't work with mock.patch.dict,
+# so we have to use the old-fashioned way of setting the environment variable
+# and then cleaning it up manually.
+#
+# @mock.patch.dict(os.environ, {"DISPATCH_API_KEY": "0000000000000000"})
 @pytest.mark.asyncio
-@mock.patch.dict(os.environ, {"DISPATCH_API_KEY": "0000000000000000"})
 async def test_api_key_from_env():
-    async with server() as api:
-        client = Client(api_url=api.url)
-
-        with pytest.raises(
-            PermissionError,
-            match=r"Dispatch received an invalid authentication token \(check DISPATCH_API_KEY is correct\)",
-        ) as mc:
-            await client.dispatch([Call(function="my-function", input=42)])
-
+    prev_api_key = os.environ.get("DISPATCH_API_KEY")
+    try:
+        os.environ["DISPATCH_API_KEY"] = "0000000000000000"
+        async with server() as api:
+            client = Client(api_url=api.url)
+
+            with pytest.raises(
+                    PermissionError,
+                    match=r"Dispatch received an invalid authentication token \(check DISPATCH_API_KEY is correct\)",
+            ) as mc:
+                await client.dispatch([Call(function="my-function", input=42)])
+    finally:
+        if prev_api_key is None:
+            del os.environ["DISPATCH_API_KEY"]
+        else:
+            os.environ["DISPATCH_API_KEY"] = prev_api_key
 
 @pytest.mark.asyncio
 async def test_api_key_from_arg():
diff --git a/tests/test_fastapi.py b/tests/test_fastapi.py
index 9c067ef..a317a9b 100644
--- a/tests/test_fastapi.py
+++ b/tests/test_fastapi.py
@@ -57,7 +57,7 @@ def dispatch_test_init(self, reg: Registry) -> str:
         self.sockets = [sock]
         self.uvicorn = uvicorn.Server(config)
         self.runner = Runner()
-        if sys.version_info >= (3, 9):
+        if sys.version_info >= (3, 10):
             self.event = asyncio.Event()
         else:
             self.event = asyncio.Event(loop=self.runner.get_loop())
diff --git a/tests/test_http.py b/tests/test_http.py
index 69ad365..cba4742 100644
--- a/tests/test_http.py
+++ b/tests/test_http.py
@@ -46,7 +46,7 @@ def dispatch_test_init(self, reg: Registry) -> str:
         self.aiohttp = Server(host, port, Dispatch(reg))
         self.aioloop.run(self.aiohttp.start())
 
-        if sys.version_info >= (3, 9):
+        if sys.version_info >= (3, 10):
             self.aiowait = asyncio.Event()
         else:
             self.aiowait = asyncio.Event(loop=self.aioloop.get_loop())