diff --git a/datasette/utils/check_callable.py b/datasette/utils/check_callable.py
index e21a769b..e3e809b2 100644
--- a/datasette/utils/check_callable.py
+++ b/datasette/utils/check_callable.py
@@ -1,5 +1,4 @@
 import inspect
-import types
 from typing import Any, NamedTuple
 
 
@@ -16,8 +15,11 @@ def check_callable(obj: Any) -> CallableStatus:
         # It's a class
         return CallableStatus(True, False)
 
-    if isinstance(obj, types.FunctionType):
-        return CallableStatus(True, inspect.iscoroutinefunction(obj))
+    if inspect.iscoroutinefunction(obj):
+        # Inspect the object itself, so bound methods and functools.partial objects
+        # wrapping an async function are recognised - they are not types.FunctionType,
+        # and their __call__ is a method wrapper rather than a coroutine function.
+        return CallableStatus(True, True)
 
     if callable(obj):
         return CallableStatus(True, inspect.iscoroutinefunction(obj.__call__))
diff --git a/tests/test_utils_check_callable.py b/tests/test_utils_check_callable.py
index 857b73cd..ebe84764 100644
--- a/tests/test_utils_check_callable.py
+++ b/tests/test_utils_check_callable.py
@@ -1,3 +1,5 @@
+import functools
+
 import pytest
 
 from datasette.utils.check_callable import check_callable
@@ -17,6 +19,14 @@ class ClassNoCall:
     pass
 
 
+class MethodHolder:
+    async def async_method(self):
+        pass
+
+    def sync_method(self):
+        pass
+
+
 async def async_func():
     pass
 
@@ -39,6 +49,12 @@ def non_async_func():
         ("", False, False),
         (1, False, False),
         (str, True, False),
+        # Bound methods and functools.partial objects are not types.FunctionType,
+        # but they are still async when the function they wrap is
+        (MethodHolder().async_method, True, True),
+        (MethodHolder().sync_method, True, False),
+        (functools.partial(async_func), True, True),
+        (functools.partial(non_async_func), True, False),
     ),
 )
 def test_check_callable(obj, expected_is_callable, expected_is_async_callable):