diff --git a/setup.py b/setup.py
index 732fa7acd7..5c5890d8a5 100644
--- a/setup.py
+++ b/setup.py
@@ -81,7 +81,7 @@
     install_requires=[
         "attrs >= 19.2.0",  # for eq
         "sortedcontainers",
-        "async_generator >= 1.9",
+        "contextlib2; python_version < '3.10'",
         "idna",
         "outcome",
         "sniffio",
diff --git a/test-requirements.in b/test-requirements.in
index 99854204d6..16463dcb47 100644
--- a/test-requirements.in
+++ b/test-requirements.in
@@ -1,12 +1,13 @@
 # For tests
-pytest >= 5.0         # for faulthandler in core
+pytest >= 5.0           # for faulthandler in core
 pytest-cov >= 2.6.0
-ipython               # for the IPython traceback integration tests
-pyOpenSSL             # for the ssl tests
-trustme               # for the ssl tests
-pylint                # for pylint finding all symbols tests
-jedi                  # for jedi code completion tests
-cryptography>=36.0.0  # 35.0.0 is transitive but fails
+ipython                 # for the IPython traceback integration tests
+pyOpenSSL               # for the ssl tests
+trustme                 # for the ssl tests
+pylint                  # for pylint finding all symbols tests
+jedi                    # for jedi code completion tests
+cryptography>=36.0.0    # 35.0.0 is transitive but fails
+async_generator >= 1.9  # for testing against py3.5 style async generator wrappers
 
 # Tools
 black; implementation_name == "cpython"
@@ -24,7 +25,7 @@ typing-extensions; implementation_name == "cpython"
 cffi; os_name == "nt"
 attrs >= 19.2.0
 sortedcontainers
-async_generator >= 1.9
+contextlib2; python_version < '3.10'
 idna
 outcome
 sniffio
diff --git a/test-requirements.txt b/test-requirements.txt
index f1162efdb0..974d3862fd 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -23,6 +23,8 @@ cffi==1.15.0
     # via cryptography
 click==8.0.3
     # via black
+contextlib2==21.6.0 ; python_version < "3.10"
+    # via -r test-requirements.in
 coverage[toml]==6.0.2
     # via pytest-cov
 cryptography==36.0.1
@@ -38,8 +40,6 @@ idna==3.3
     # via
     #   -r test-requirements.in
     #   trustme
-immutables==0.16
-    # via -r test-requirements.in
 importlib-metadata==4.2.0
     # via
     #   click
@@ -149,7 +149,6 @@ typing-extensions==3.10.0.2 ; implementation_name == "cpython"
     #   -r test-requirements.in
     #   astroid
     #   black
-    #   immutables
     #   importlib-metadata
     #   mypy
     #   pylint
diff --git a/trio/_core/_ki.py b/trio/_core/_ki.py
index 36aacecd96..fdf396a3a3 100644
--- a/trio/_core/_ki.py
+++ b/trio/_core/_ki.py
@@ -4,8 +4,6 @@
 from functools import wraps
 import attr
 
-import async_generator
-
 from .._util import is_main_thread
 
 if False:
@@ -141,7 +139,7 @@ def wrapper(*args, **kwargs):
                 return gen
 
             return wrapper
-        elif async_generator.isasyncgenfunction(fn):
+        elif inspect.isasyncgenfunction(fn):
 
             @wraps(fn)
             def wrapper(*args, **kwargs):
diff --git a/trio/_core/tests/test_asyncgen.py b/trio/_core/tests/test_asyncgen.py
index 6ce0af366f..983c2852c1 100644
--- a/trio/_core/tests/test_asyncgen.py
+++ b/trio/_core/tests/test_asyncgen.py
@@ -2,11 +2,14 @@
 import weakref
 import pytest
 from math import inf
-from functools import partial
-from async_generator import aclosing
 from ... import _core
 from .tutil import gc_collect_harder, buggy_pypy_asyncgens, restore_unraisablehook
 
+if sys.version_info >= (3, 10):
+    from contextlib import aclosing
+else:
+    from contextlib2 import aclosing
+
 
 def test_asyncgen_basics():
     collected = []
diff --git a/trio/_util.py b/trio/_util.py
index b5a2ceabdc..deebd66a7e 100644
--- a/trio/_util.py
+++ b/trio/_util.py
@@ -5,14 +5,11 @@
 from abc import ABCMeta
 import os
 import signal
-import sys
-import pathlib
-from functools import wraps, update_wrapper
+from functools import update_wrapper
 import typing as t
 import threading
 import collections
-
-from async_generator import isasyncgen
+from inspect import isasyncgen
 
 import trio
 
@@ -334,8 +331,4 @@ def name_asyncgen(agen):
         module = agen.ag_frame.f_globals["__name__"]
     except (AttributeError, KeyError):
         module = "<{}>".format(agen.ag_code.co_filename)
-    try:
-        qualname = agen.__qualname__
-    except AttributeError:
-        qualname = agen.ag_code.co_name
-    return f"{module}.{qualname}"
+    return f"{module}.{agen.__qualname__}"
diff --git a/trio/testing/_sequencer.py b/trio/testing/_sequencer.py
index a7e6e50ff0..c4e34717a1 100644
--- a/trio/testing/_sequencer.py
+++ b/trio/testing/_sequencer.py
@@ -1,7 +1,7 @@
 from collections import defaultdict
+from contextlib import asynccontextmanager
 
 import attr
-from async_generator import asynccontextmanager
 
 from .. import _core
 from .. import _util
diff --git a/trio/tests/test_ssl.py b/trio/tests/test_ssl.py
index 10e6c13d8f..fee4063b74 100644
--- a/trio/tests/test_ssl.py
+++ b/trio/tests/test_ssl.py
@@ -6,12 +6,11 @@
 import threading
 import socket as stdlib_socket
 import ssl
-from contextlib import contextmanager
+from contextlib import asynccontextmanager, contextmanager
 from functools import partial
 
 from OpenSSL import SSL
 import trustme
-from async_generator import asynccontextmanager
 
 import trio
 from .. import _core
diff --git a/trio/tests/test_subprocess.py b/trio/tests/test_subprocess.py
index 65abe13e50..6065c3f11c 100644
--- a/trio/tests/test_subprocess.py
+++ b/trio/tests/test_subprocess.py
@@ -3,11 +3,11 @@
 import signal
 import subprocess
 import sys
+from contextlib import asynccontextmanager
 from functools import partial
 from pathlib import Path as SyncPath
 
 import pytest
-from async_generator import asynccontextmanager
 
 from .. import (
     ClosedResourceError,