diff --git a/Lib/pydoc.py b/Lib/pydoc.py
--- a/Lib/pydoc.py
+++ b/Lib/pydoc.py
@@ -220,39 +220,40 @@
     else: result = None
     return result
 
+def _synopsis(filename):
+    # Look for binary suffixes first.
+    if any(filename.endswith(suffix)
+           for suffix in importlib.machinery.BYTECODE_SUFFIXES):
+        loader_cls = importlib.machinery.SourcelessFileLoader
+    elif any(filename.endswith(suffix)
+             for suffix in importlib.machinery.EXTENSION_SUFFIXES):
+        loader_cls = importlib.machinery.ExtensionFileLoader
+    else:
+        # Must be a source file.
+        try:
+            file = tokenize.open(filename)
+        except OSError:
+            # module can't be opened, so skip it
+            return None
+        # text modules can be directly examined
+        with file:
+            return source_synopsis(file)
+
+    # Must be a binary module, which has to be imported.
+    loader = loader_cls('__temp__', filename)
+    try:
+        module = loader.load_module('__temp__')
+    except:
+        return None
+    del sys.modules['__temp__']
+    return (module.__doc__ or '').splitlines()[0]
+
 def synopsis(filename, cache={}):
     """Get the one-line summary out of a module file."""
     mtime = os.stat(filename).st_mtime
     lastupdate, result = cache.get(filename, (None, None))
     if lastupdate is None or lastupdate < mtime:
-        try:
-            file = tokenize.open(filename)
-        except OSError:
-            # module can't be opened, so skip it
-            return None
-        binary_suffixes = importlib.machinery.BYTECODE_SUFFIXES[:]
-        binary_suffixes += importlib.machinery.EXTENSION_SUFFIXES[:]
-        if any(filename.endswith(x) for x in binary_suffixes):
-            # binary modules have to be imported
-            file.close()
-            if any(filename.endswith(x) for x in
-                    importlib.machinery.BYTECODE_SUFFIXES):
-                loader = importlib.machinery.SourcelessFileLoader('__temp__',
-                                                                  filename)
-            else:
-                loader = importlib.machinery.ExtensionFileLoader('__temp__',
-                                                                 filename)
-            try:
-                module = loader.load_module('__temp__')
-            except:
-                return None
-            result = (module.__doc__ or '').splitlines()[0]
-            del sys.modules['__temp__']
-        else:
-            # text modules can be directly examined
-            result = source_synopsis(file)
-            file.close()
-
+        result = _synopsis(filename)
         cache[filename] = (mtime, result)
     return result
 
diff --git a/Lib/test/test_pydoc.py b/Lib/test/test_pydoc.py
--- a/Lib/test/test_pydoc.py
+++ b/Lib/test/test_pydoc.py
@@ -487,6 +487,13 @@
             synopsis = pydoc.synopsis(TESTFN, {})
             self.assertEqual(synopsis, 'line 1: h\xe9')
 
+    def test_synopsis_sourceless(self):
+        expected = os.__doc__.splitlines()[0]
+        filename = os.__cached__
+        synopsis = pydoc.synopsis(filename)
+
+        self.assertEqual(synopsis, expected)
+
     def test_splitdoc_with_description(self):
         example_string = "I Am A Doc\n\n\nHere is my description"
         self.assertEqual(pydoc.splitdoc(example_string),
@@ -600,6 +607,50 @@
         self.assertEqual(out.getvalue(), '')
         self.assertEqual(err.getvalue(), '')
 
+    def test_modules(self):
+        # See Helper.listmodules().
+        num_header_lines = 2
+        num_module_lines_min = 5  # Playing it safe.
+        num_footer_lines = 3
+        expected = num_header_lines + num_module_lines_min + num_footer_lines
+
+        output = StringIO()
+        helper = pydoc.Helper(output=output)
+        helper('modules')
+        result = output.getvalue().strip()
+        num_lines = len(result.splitlines())
+
+        self.assertGreaterEqual(num_lines, expected)
+
+    def test_modules_search(self):
+        # See Helper.listmodules().
+        expected = 'pydoc - '
+
+        output = StringIO()
+        helper = pydoc.Helper(output=output)
+        with captured_stdout() as help_io:
+            helper('modules pydoc')
+        result = help_io.getvalue()
+
+        self.assertIn(expected, result)
+
+    def test_modules_search_builtin(self):
+        expected = 'gc - '
+
+        output = StringIO()
+        helper = pydoc.Helper(output=output)
+        with captured_stdout() as help_io:
+            helper('modules garbage')
+        result = help_io.getvalue()
+
+        self.assertTrue(result.startswith(expected))
+
+    def test_importfile(self):
+        loaded_pydoc = pydoc.importfile(pydoc.__file__)
+
+        self.assertEqual(loaded_pydoc.__name__, 'pydoc')
+        self.assertEqual(loaded_pydoc.__file__, pydoc.__file__)
+
 
 class TestDescriptions(unittest.TestCase):
 
@@ -827,6 +878,7 @@
             print_diffs(expected_text, result)
             self.fail("outputs are not equal, see diff above")
 
+
 @reap_threads
 def test_main():
     try:
diff --git a/Misc/NEWS b/Misc/NEWS
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -221,6 +221,8 @@
 - Issue #19782: imaplib now supports SSLContext.check_hostname and server name
   indication for TLS/SSL connections.
 
+- Issue 20123: Fix pydoc.synopsis() for "binary" modules.
+
 - Issue #19834: Support unpickling of exceptions pickled by Python 2.
 
 - Issue #19781: ftplib now supports SSLContext.check_hostname and server name