diff --git a/bitmask.py b/bitmask.py
index 5ace01c..f03451a 100644
--- a/bitmask.py
+++ b/bitmask.py
@@ -171,14 +171,40 @@ class Bitmask:
         return self.__mask_op(other, lambda a, b : a | b)
 
     def __radd__(self, other):
+        """Alias the + operator in reverse."""
         return self.__add__(other)
 
+    def __iadd__(self, other):
+        """Union bitmasks/flags together.
+
+        Aliased to `Bitmask.__add__`.
+        """
+        return self + other
+
+    def __sub__(self, other):
+        """Subtract by bitmask/flag."""
+        return self.__mask_op(other, lambda a, b : a & ~b)
+
+    def __isub__(self, other):
+        """Subtract a bitmask/flag.
+
+        Aliased to `Bitmask.__sub__`.
+        """
+        self = self - other
+        return self
+
     def discard(self, flag):
         """Remove flag bitmask if present.
 
         This behaves the same as built-in `set.discard()`.
+
+        Raises:
+            TypeError: `flag` is not a single Enum value.
         """
-        self._flag_op(flag, lambda a, b : a & ~b)
+        if not issubclass(type(flag), self._AllFlags):
+            raise TypeError(f"can only discard {self.AllFlags} (not '{type(flag)}') from {type(self)}")
+
+        return self._flag_op(flag, lambda a, b : a & ~b)
 
     def remove(self, flag):
         """Remove `flag` from the bitmask.
@@ -189,5 +215,6 @@ class Bitmask:
             KeyError: flag is not in bitmask.
         """
         if not flag in self:
-            raise KeyError(flag)
+            raise KeyError(type(flag), self.AllFlags)
+
         self.discard(flag)
diff --git a/test_bitmask.py b/test_bitmask.py
index 8982642..bd6a0c9 100644
--- a/test_bitmask.py
+++ b/test_bitmask.py
@@ -76,6 +76,8 @@ class TestBitmask(unittest.TestCase):
             self.bmask.remove(Desc.SMALL)
         with self.assertRaises(KeyError):
             self.bmask_empty.remove(Desc.SMALL)
+        with self.assertRaises(TypeError):
+            self.bmask_empty.remove(self.bmask2)
     
     def test_discard(self):
         """Test the `Bitmask.discard()` method."""
@@ -94,6 +96,22 @@ class TestBitmask(unittest.TestCase):
             self.bmask_empty,
             Bitmask(Desc)
         )
+        with self.assertRaises(TypeError):
+            self.bmask_empty.remove(self.bmask2)
+
+    def test_subtract(self):
+        """Test various subtraction operators."""
+        # Operation
+        self.assertEqual(
+            self.bmask - Desc.SMALL,
+            Bitmask(Desc, Desc.FUNKY)
+        )
+        # Assignment
+        self.bmask -= Desc.SMALL
+        self.assertEqual(
+            self.bmask,
+            Bitmask(Desc, Desc.FUNKY)
+        )
 
     def test_value(self):
         """Ensure Bitmask.value lines up with the state."""