diff --git a/Lib/dbm/__init__.py b/Lib/dbm/__init__.py
index 56555be..c224847 100644
--- a/Lib/dbm/__init__.py
+++ b/Lib/dbm/__init__.py
@@ -36,7 +36,7 @@
 only if it doesn't exist; and 'n' always creates a new database.
 """
 
-__all__ = ['open', 'whichdb', 'error', 'errors']
+__all__ = ['open', 'whichdb', 'error', 'error']
 
 import io
 import os
diff --git a/Lib/test/test___all__.py b/Lib/test/test___all__.py
index a4e69b2..200db5c 100644
--- a/Lib/test/test___all__.py
+++ b/Lib/test/test___all__.py
@@ -1,9 +1,17 @@
 import unittest
-from test.support import run_unittest
+from test import support
+import os
 import sys
 import warnings
 
 
+class NoAll(RuntimeError):
+    pass
+
+class FailedImport(RuntimeError):
+    pass
+
+
 class AllTest(unittest.TestCase):
 
     def check_all(self, modname):
@@ -13,153 +21,97 @@
                                     DeprecationWarning)
             try:
                 exec("import %s" % modname, names)
-            except ImportError:
+            except:
                 # Silent fail here seems the best route since some modules
-                # may not be available in all environments.
-                return
-        self.assertTrue(hasattr(sys.modules[modname], "__all__"),
-                        "%s has no __all__ attribute" % modname)
+                # may not be available or not initialize properly in all
+                # environments.
+                raise FailedImport(modname)
+        if not hasattr(sys.modules[modname], "__all__"):
+            raise NoAll(modname)
         names = {}
-        exec("from %s import *" % modname, names)
+        try:
+            exec("from %s import *" % modname, names)
+        except Exception as e:
+            # Include the module name in the exception string
+            self.fail("__all__ failure in {}: {}: {}".format(
+                      modname, e.__class__.__name__, e))
         if "__builtins__" in names:
             del names["__builtins__"]
         keys = set(names)
         all = set(sys.modules[modname].__all__)
         self.assertEqual(keys, all)
 
+    def walk_modules(self, basedir, modpath):
+        for fn in sorted(os.listdir(basedir)):
+            path = os.path.join(basedir, fn)
+            if os.path.isdir(path):
+                pkg_init = os.path.join(path, '__init__.py')
+                if os.path.exists(pkg_init):
+                    yield pkg_init, modpath + fn
+                    for p, m in self.walk_modules(path, modpath + fn + "."):
+                        yield p, m
+                continue
+            if not fn.endswith('.py') or fn == '__init__.py':
+                continue
+            yield path, modpath + fn[:-3]
+
     def test_all(self):
+        # Blacklisted modules and packages
+        blacklist = set([
+            # Will raise a SyntaxError when compiling the exec statement
+            '__future__',
+        ])
+
         if not sys.platform.startswith('java'):
             # In case _socket fails to build, make this test fail more gracefully
             # than an AttributeError somewhere deep in CGIHTTPServer.
             import _socket
 
-        self.check_all("http.server")
-        self.check_all("configparser")
-        self.check_all("http.cookies")
-        self.check_all("queue")
-        self.check_all("socketserver")
-        self.check_all("aifc")
-        self.check_all("base64")
-        self.check_all("bdb")
-        self.check_all("binhex")
-        self.check_all("calendar")
-        self.check_all("collections")
-        self.check_all("cgi")
-        self.check_all("cmd")
-        self.check_all("code")
-        self.check_all("codecs")
-        self.check_all("codeop")
-        self.check_all("colorsys")
-        self.check_all("compileall")
-        self.check_all("copy")
-        self.check_all("copyreg")
-        self.check_all("csv")
-        self.check_all("dbm.bsd")
-        self.check_all("decimal")
-        self.check_all("difflib")
-        self.check_all("dircache")
-        self.check_all("dis")
-        self.check_all("doctest")
-        self.check_all("_dummy_thread")
-        self.check_all("dummy_threading")
-        self.check_all("filecmp")
-        self.check_all("fileinput")
-        self.check_all("fnmatch")
-        self.check_all("fpformat")
-        self.check_all("ftplib")
-        self.check_all("getopt")
-        self.check_all("getpass")
-        self.check_all("gettext")
-        self.check_all("glob")
-        self.check_all("gzip")
-        self.check_all("heapq")
-        self.check_all("http.client")
-        self.check_all("ihooks")
-        self.check_all("io")
-        self.check_all("_pyio")
-        self.check_all("imaplib")
-        self.check_all("imghdr")
-        self.check_all("keyword")
-        self.check_all("linecache")
-        self.check_all("locale")
-        self.check_all("logging")
-        self.check_all("macpath")
-        self.check_all("macurl2path")
-        self.check_all("mailbox")
-        self.check_all("mailcap")
-        self.check_all("mhlib")
-        self.check_all("mimetypes")
-        self.check_all("multifile")
-        self.check_all("netrc")
-        self.check_all("nntplib")
-        self.check_all("ntpath")
-        self.check_all("opcode")
-        self.check_all("optparse")
-        self.check_all("os")
-        self.check_all("os2emxpath")
-        self.check_all("pdb")
-        self.check_all("pickle")
-        self.check_all("pickletools")
-        self.check_all("pipes")
-        self.check_all("poplib")
-        self.check_all("posixpath")
-        self.check_all("pprint")
-        self.check_all("profile")
-        self.check_all("pstats")
-        self.check_all("pty")
-        self.check_all("py_compile")
-        self.check_all("pyclbr")
-        self.check_all("quopri")
-        self.check_all("random")
-        self.check_all("re")
-        self.check_all("reprlib")
-        self.check_all("rlcompleter")
-        self.check_all("urllib.robotparser")
-        self.check_all("sched")
-        self.check_all("shelve")
-        self.check_all("shlex")
-        self.check_all("shutil")
-        self.check_all("smtpd")
-        self.check_all("smtplib")
-        self.check_all("sndhdr")
-        self.check_all("socket")
-        self.check_all("_strptime")
-        self.check_all("symtable")
-        self.check_all("tabnanny")
-        self.check_all("tarfile")
-        self.check_all("telnetlib")
-        self.check_all("tempfile")
-        self.check_all("test.support")
-        self.check_all("textwrap")
-        self.check_all("threading")
-        self.check_all("timeit")
-        self.check_all("tokenize")
-        self.check_all("traceback")
-        self.check_all("tty")
-        self.check_all("unittest")
-        self.check_all("uu")
-        self.check_all("warnings")
-        self.check_all("wave")
-        self.check_all("weakref")
-        self.check_all("webbrowser")
-        self.check_all("xdrlib")
-        self.check_all("zipfile")
-
         # rlcompleter needs special consideration; it import readline which
         # initializes GNU readline which calls setlocale(LC_CTYPE, "")... :-(
         try:
-            self.check_all("rlcompleter")
-        finally:
+            import rlcompleter
+            import locale
+        except ImportError:
+            pass
+        else:
+            locale.setlocale(locale.LC_CTYPE, 'C')
+
+        ignored = []
+        failed_imports = []
+        lib_dir = os.path.dirname(os.path.dirname(__file__))
+        for path, modname in self.walk_modules(lib_dir, ""):
+            m = modname
+            blacklisted = False
+            while m:
+                if m in blacklist:
+                    blacklisted = True
+                    break
+                m = m.rpartition('.')[0]
+            if blacklisted:
+                continue
+            if support.verbose:
+                print(modname)
             try:
-                import locale
-            except ImportError:
-                pass
-            else:
-                locale.setlocale(locale.LC_CTYPE, 'C')
+                # This heuristic speeds up the process by removing, de facto,
+                # most test modules (and avoiding the auto-executing ones).
+                with open(path, "rb") as f:
+                    if b"__all__" not in f.read():
+                        raise NoAll(modname)
+                    self.check_all(modname)
+            except NoAll:
+                ignored.append(modname)
+            except FailedImport:
+                failed_imports.append(modname)
+
+        if support.verbose:
+            print('Following modules have no __all__ and have been ignored:',
+                  ignored)
+            print('Following modules failed to be imported:', failed_imports)
 
 
 def test_main():
-    run_unittest(AllTest)
+    support.run_unittest(AllTest)
 
 if __name__ == "__main__":
     test_main()
diff --git a/Misc/NEWS b/Misc/NEWS
index becd5b1..f075eb4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -108,6 +108,9 @@
 Tests
 -----
 
+- Issue #7055: test___all__ now greedily detects all modules which have an
+  __all__ attribute, rather than using a hardcoded and incomplete list.
+
 - Issue #7058: Added save/restore for argv and os.environ to runtest_inner
   in regrtest, with warnings if the called test modifies them.