diff --git a/CHANGES.rst b/CHANGES.rst
index 25463fe3c..db9877435 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -25,8 +25,13 @@ Unreleased
   1381`_ and `pull 1388`_).  Slightly improved performance when using the C
   trace function, as most environments do.
 
+- The conditions for using tomllib from the standard library have been made
+  more precise, so that 3.11 alphas will continue to work. Closes `issue
+  1390`_.
+
 .. _pull 1381: https://github.com/nedbat/coveragepy/pull/1381
 .. _pull 1388: https://github.com/nedbat/coveragepy/pull/1388
+.. _issue 1390: https://github.com/nedbat/coveragepy/issues/1390
 
 
 .. _changes_64:
diff --git a/coverage/tomlconfig.py b/coverage/tomlconfig.py
index b04d66e24..148c34f89 100644
--- a/coverage/tomlconfig.py
+++ b/coverage/tomlconfig.py
@@ -12,7 +12,7 @@
 from coverage.misc import import_third_party, substitute_variables
 
 
-if env.PYVERSION >= (3, 11):
+if env.PYVERSION >= (3, 11, 0, "alpha", 7):
     import tomllib      # pylint: disable=import-error
 else:
     # TOML support on Python 3.10 and below is an install-time extra option.
diff --git a/setup.py b/setup.py
index 969592502..67aedc1bf 100644
--- a/setup.py
+++ b/setup.py
@@ -108,7 +108,7 @@ def better_set_verbosity(v):
 
     extras_require={
         # Enable pyproject.toml support.
-        'toml': ['tomli; python_version < "3.11"'],
+        'toml': ['tomli; python_full_version<="3.11.0a6"'],
     },
 
     # We need to get HTML assets from our htmlfiles directory.