diff --git a/README.rst b/README.rst
index 5bc908d..a11ebc1 100644
--- a/README.rst
+++ b/README.rst
@@ -224,6 +224,12 @@ MIT
 Change Log
 ----------
 
+Unreleased
+~~~~~~~~~~
+
+* Update B014: ``binascii.Error`` is now treated as a subclass of ``ValueError``
+  (#206)
+
 21.9.2
 ~~~~~~~~~~
 
diff --git a/bugbear.py b/bugbear.py
index 9211495..cbfdbbe 100644
--- a/bugbear.py
+++ b/bugbear.py
@@ -193,13 +193,12 @@ def visit_ExceptHandler(self, node):
                 good = sorted(set(names), key=names.index)
                 if "BaseException" in good:
                     good = ["BaseException"]
-                # Find and remove aliases exceptions and only leave the primary alone
-                primaries = filter(
-                    lambda primary: primary in good, B014.exception_aliases.keys()
-                )
-                for primary in primaries:
-                    aliases = B014.exception_aliases[primary]
-                    good = list(filter(lambda e: e not in aliases, good))
+                # Remove redundant exceptions that the automatic system either handles
+                # poorly (usually aliases) or can't be checked (e.g. it's not an
+                # built-in exception).
+                for primary, equivalents in B014.redundant_exceptions.items():
+                    if primary in good:
+                        good = [g for g in good if g not in equivalents]
 
                 for name, other in itertools.permutations(tuple(good), 2):
                     if _typesafe_issubclass(
@@ -758,15 +757,19 @@ def visit(self, node):
         "Write `except {2}{1}:`, which catches exactly the same exceptions."
     )
 )
-B014.exception_aliases = {
+B014.redundant_exceptions = {
     "OSError": {
+        # All of these are actually aliases of OSError since Python 3.3
         "IOError",
         "EnvironmentError",
         "WindowsError",
         "mmap.error",
         "socket.error",
         "select.error",
-    }
+    },
+    "ValueError": {
+        "binascii.Error",
+    },
 }
 B015 = Error(
     message=(
diff --git a/tests/b014.py b/tests/b014.py
index 0144762..3847345 100644
--- a/tests/b014.py
+++ b/tests/b014.py
@@ -1,8 +1,9 @@
 """
 Should emit:
-B014 - on lines 10, 16, 27, 41, 48, and 55
+B014 - on lines 11, 17, 28, 42, 49, 56, and 74.
 """
 
+import binascii
 import re
 
 try:
@@ -66,3 +67,10 @@ class MyError(Exception):
 except (MyException, NotImplemented):
     # NotImplemented is not an exception, let's not crash on it.
     pass
+
+
+try:
+    pass
+except (ValueError, binascii.Error):
+    # binascii.Error is a subclass of ValueError.
+    pass
diff --git a/tests/test_bugbear.py b/tests/test_bugbear.py
index c9540a3..4cd01b9 100644
--- a/tests/test_bugbear.py
+++ b/tests/test_bugbear.py
@@ -179,16 +179,17 @@ def test_b014(self):
         bbc = BugBearChecker(filename=str(filename))
         errors = list(bbc.run())
         expected = self.errors(
-            B014(10, 0, vars=("Exception, TypeError", "", "Exception")),
-            B014(16, 0, vars=("OSError, OSError", " as err", "OSError")),
-            B014(27, 0, vars=("MyError, MyError", "", "MyError")),
-            B014(41, 0, vars=("MyError, BaseException", " as e", "BaseException")),
-            B014(48, 0, vars=("re.error, re.error", "", "re.error")),
+            B014(11, 0, vars=("Exception, TypeError", "", "Exception")),
+            B014(17, 0, vars=("OSError, OSError", " as err", "OSError")),
+            B014(28, 0, vars=("MyError, MyError", "", "MyError")),
+            B014(42, 0, vars=("MyError, BaseException", " as e", "BaseException")),
+            B014(49, 0, vars=("re.error, re.error", "", "re.error")),
             B014(
-                55,
+                56,
                 0,
                 vars=("IOError, EnvironmentError, OSError", "", "OSError"),
             ),
+            B014(74, 0, vars=("ValueError, binascii.Error", "", "ValueError")),
         )
         self.assertEqual(errors, expected)