diff --git a/CHANGES.rst b/CHANGES.rst
index b493f68e7..b7e8fd27b 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -23,6 +23,10 @@ Unreleased
 - Fix: the PyPI page had broken links to documentation pages, but no longer
   does, closing `issue 1566`_.
 
+- Fix: public members of the coverage module are now properly indicated so that
+  mypy will find them, fixing `issue 1564`_.
+
+.. _issue 1564: https://github.com/nedbat/coveragepy/issues/1564
 .. _issue 1566: https://github.com/nedbat/coveragepy/issues/1566
 
 
diff --git a/coverage/__init__.py b/coverage/__init__.py
index efd0a6f03..054e37dff 100644
--- a/coverage/__init__.py
+++ b/coverage/__init__.py
@@ -9,15 +9,29 @@
 
 """
 
-import sys
+# mypy's convention is that "import as" names are public from the module.
+# We import names as themselves to indicate that. Pylint sees it as pointless,
+# so disable its warning.
+# pylint: disable=useless-import-alias
 
-from coverage.version import __version__, __url__, version_info
+import sys
 
-from coverage.control import Coverage, process_startup
-from coverage.data import CoverageData
-from coverage.exceptions import CoverageException
-from coverage.plugin import CoveragePlugin, FileTracer, FileReporter
-from coverage.pytracer import PyTracer
+from coverage.version import (
+    __version__ as __version__,
+    version_info as version_info,
+)
+
+from coverage.control import (
+    Coverage as Coverage,
+    process_startup as process_startup,
+)
+from coverage.data import CoverageData as CoverageData
+from coverage.exceptions import CoverageException as CoverageException
+from coverage.plugin import (
+    CoveragePlugin as CoveragePlugin,
+    FileReporter as FileReporter,
+    FileTracer as FileTracer,
+)
 
 # Backward compatibility.
 coverage = Coverage
diff --git a/coverage/cmdline.py b/coverage/cmdline.py
index 338d8a25a..ef760a503 100644
--- a/coverage/cmdline.py
+++ b/coverage/cmdline.py
@@ -27,6 +27,7 @@
 from coverage.exceptions import _BaseCoverageException, _ExceptionDuringRun, NoSource
 from coverage.execfile import PyRunner
 from coverage.results import Numbers, should_fail_under
+from coverage.version import __url__
 
 # When adding to this file, alphabetization is important.  Look for
 # "alphabetize" comments throughout.
@@ -574,6 +575,7 @@ def show_help(
             program_name = program_name[:-len(auto_suffix)]
 
     help_params = dict(coverage.__dict__)
+    help_params["__url__"] = __url__
     help_params['program_name'] = program_name
     if HAS_CTRACER:
         help_params['extension_modifier'] = 'with C extension'
diff --git a/coverage/html.py b/coverage/html.py
index 9e1b11b20..ae09bc37d 100644
--- a/coverage/html.py
+++ b/coverage/html.py
@@ -24,6 +24,7 @@
 from coverage.results import Analysis, Numbers
 from coverage.templite import Templite
 from coverage.types import TLineNo, TMorf
+from coverage.version import __url__
 
 
 if TYPE_CHECKING:
@@ -238,7 +239,7 @@ def __init__(self, cov: Coverage) -> None:
             'len': len,
 
             # Constants for this report.
-            '__url__': coverage.__url__,
+            '__url__': __url__,
             '__version__': coverage.__version__,
             'title': title,
             'time_stamp': format_local_datetime(datetime.datetime.now()),
diff --git a/coverage/xmlreport.py b/coverage/xmlreport.py
index 6867f2e92..65da11d23 100644
--- a/coverage/xmlreport.py
+++ b/coverage/xmlreport.py
@@ -14,12 +14,13 @@
 from dataclasses import dataclass
 from typing import Any, Dict, IO, Iterable, Optional, TYPE_CHECKING, cast
 
-from coverage import __url__, __version__, files
+from coverage import __version__, files
 from coverage.misc import isolate_module, human_sorted, human_sorted_items
 from coverage.plugin import FileReporter
 from coverage.report import get_analysis_to_report
 from coverage.results import Analysis
 from coverage.types import TMorf
+from coverage.version import __url__
 
 if TYPE_CHECKING:
     from coverage import Coverage