diff --git a/CHANGES.rst b/CHANGES.rst
index f056ddd6d..69eed03b2 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -20,8 +20,15 @@ development at the same time, such as 4.5.x and 5.0.
 Unreleased
 ----------
 
-Nothing yet.
+- The semantics of stars in file patterns has been clarified in the docs.  A
+  leading or trailing star matches any number of path components, like a double
+  star would.  This is different than the behavior of a star in the middle of a
+  pattern.  This discrepancy was `identified by Sviatoslav Sydorenko
+  <starbad_>`_, who `provided patient detailed diagnosis <pull 1650_>`_ and
+  graciously agreed to a pragmatic resolution.
 
+.. _starbad: https://github.com/nedbat/coveragepy/issues/1407#issuecomment-1631085209
+.. _pull 1650: https://github.com/nedbat/coveragepy/pull/1650
 
 .. scriv-start-here
 
@@ -32,7 +39,7 @@ Version 7.3.0 — 2023-08-12
 
 - Added a :meth:`.Coverage.collect` context manager to start and stop coverage
   data collection.
-  
+
 - Dropped support for Python 3.7.
 
 - Fix: in unusual circumstances, SQLite cannot be set to asynchronous mode.
diff --git a/doc/_static/coverage.css b/doc/_static/coverage.css
index ee5349910..43d2ae12e 100644
--- a/doc/_static/coverage.css
+++ b/doc/_static/coverage.css
@@ -66,6 +66,16 @@ img.tideliftlogo {
     background: #efc;
 }
 
+/* I'm not sure why I had to make this so specific to get it to take effect... */
+div.rst-content div.document div.wy-table-responsive table.docutils.align-default tbody tr td {
+    vertical-align: top !important;
+}
+
+/* And this doesn't work, and I guess I just have to live with it. */
+div.rst-content div.document div.wy-table-responsive table.docutils.align-default tbody tr td .line-block {
+    margin-bottom: 0 !important;
+}
+
 /* sphinx-code-tabs */
 
 /* Some selectors here are extra-specific (.container) because this file comes
diff --git a/doc/source.rst b/doc/source.rst
index 44b84f001..3357ae73d 100644
--- a/doc/source.rst
+++ b/doc/source.rst
@@ -178,15 +178,67 @@ individual source lines.  See :ref:`excluding` for details.
 File patterns
 -------------
 
-File path patterns are used for include and omit, and for combining path
-remapping.  They follow common shell syntax:
-
-- ``*`` matches any number of file name characters, not including the directory
-  separator.
+File path patterns are used for :ref:`include <config_run_include>` and
+:ref:`omit <config_run_omit>`, and for :ref:`combining path remapping
+<cmd_combine_remapping>`.  They follow common shell syntax:
 
 - ``?`` matches a single file name character.
 
-- ``**`` matches any number of nested directory names, including none.
+- ``*`` matches any number of file name characters, not including the directory
+  separator.  As a special case, if a pattern starts with ``*/``, it is treated
+  as ``**/``, and if a pattern ends with ``/*``, it is treated as ``/**``.
+
+- ``**`` matches any number of nested directory names, including none. It must
+  be used as a full component of the path, not as part of a word: ``/**/`` is
+  allowed, but ``/a**/`` is not.
 
 - Both ``/`` and ``\`` will match either a slash or a backslash, to make
   cross-platform matching easier.
+
+- A pattern with no directory separators matches the file name in any
+  directory.
+
+Some examples:
+
+.. list-table::
+    :widths: 20 20 20
+    :header-rows: 1
+
+    * - Pattern
+      - Matches
+      - Doesn't Match
+    * - ``a*.py``
+      - | anything.py
+        | sub1/sub2/another.py
+      - | cat.py
+    * - ``sub/*/*.py``
+      - | sub/a/main.py
+        | sub/b/another.py
+      - | sub/foo.py
+        | sub/m1/m2/foo.py
+    * - ``sub/**/*.py``
+      - | sub/something.py
+        | sub/a/main.py
+        | sub/b/another.py
+        | sub/m1/m2/foo.py
+      - | sub1/anything.py
+        | sub1/more/code/main.py
+    * - ``*/sub/*``
+      - | some/where/sub/more/something.py
+        | sub/hello.py
+      - | sub1/anything.py
+    * - ``*/sub*/*``
+      - | some/where/sub/more/something.py
+        | sub/hello.py
+        | sub1/anything.py
+      - | some/more/something.py
+    * - ``*/*sub/test_*.py``
+      - | some/where/sub/test_everything.py
+        | moresub/test_things.py
+      - | some/where/sub/more/test_everything.py
+        | more/test_things.py
+    * - ``*/*sub/*sub/**``
+      - | sub/sub/something.py
+        | asub/bsub/more/thing.py
+        | code/sub/sub/code.py
+      - | sub/something.py
diff --git a/tests/test_files.py b/tests/test_files.py
index ae3a5e2b2..09da65c20 100644
--- a/tests/test_files.py
+++ b/tests/test_files.py
@@ -235,9 +235,24 @@ def globs_to_regex_params(
         ),
         globs_to_regex_params(
             ["*/foo"], case_insensitive=False, partial=True,
-            matches=["abc/foo/hi.py", "foo/hi.py"],
+            matches=["abc/foo/hi.py", "foo/hi.py", "abc/def/foo/hi.py"],
             nomatches=["abc/xfoo/hi.py"],
         ),
+        globs_to_regex_params(
+            ["*c/foo"], case_insensitive=False, partial=True,
+            matches=["abc/foo/hi.py"],
+            nomatches=["abc/xfoo/hi.py", "foo/hi.py", "def/abc/foo/hi.py"],
+        ),
+        globs_to_regex_params(
+            ["foo/x*"], case_insensitive=False, partial=True,
+            matches=["foo/x", "foo/xhi.py", "foo/x/hi.py"],
+            nomatches=[],
+        ),
+        globs_to_regex_params(
+            ["foo/x*"], case_insensitive=False, partial=False,
+            matches=["foo/x", "foo/xhi.py"],
+            nomatches=["foo/x/hi.py"],
+        ),
         globs_to_regex_params(
             ["**/foo"],
             matches=["foo", "hello/foo", "hi/there/foo"],