diff --git a/humanfriendly/case.py b/humanfriendly/case.py
index 4c71857..010a5a0 100644
--- a/humanfriendly/case.py
+++ b/humanfriendly/case.py
@@ -33,6 +33,8 @@
 # Public identifiers that require documentation.
 __all__ = ("CaseInsensitiveDict", "CaseInsensitiveKey")
 
+_MISSING = object()
+
 
 class CaseInsensitiveDict(collections.OrderedDict):
 
@@ -74,8 +76,10 @@ def get(self, key, default=None):
         """Get the value of an existing item."""
         return super(CaseInsensitiveDict, self).get(self.coerce_key(key), default)
 
-    def pop(self, key, default=None):
+    def pop(self, key, default=_MISSING):
         """Remove an item from a case insensitive dictionary."""
+        if default is _MISSING:
+            return super(CaseInsensitiveDict, self).pop(self.coerce_key(key))
         return super(CaseInsensitiveDict, self).pop(self.coerce_key(key), default)
 
     def setdefault(self, key, default=None):
@@ -95,7 +99,7 @@ def update(self, other=None, **kw):
         elif other is not None:
             # Complain about unsupported values.
             msg = "'%s' object is not iterable"
-            type_name = type(value).__name__
+            type_name = type(other).__name__
             raise TypeError(msg % type_name)
         # Copy the keyword arguments (if any).
         for key, value in kw.items():
diff --git a/humanfriendly/tests.py b/humanfriendly/tests.py
index 72dad99..a7a8375 100644
--- a/humanfriendly/tests.py
+++ b/humanfriendly/tests.py
@@ -172,6 +172,21 @@ def test_case_insensitive_dict(self):
         obj['Existing_Key'] = 11
         assert obj['existing_key'] == 11
 
+    def test_case_insensitive_pop_missing(self):
+        """Preserve the distinction between a missing and an explicit default."""
+        obj = CaseInsensitiveDict()
+        self.assertRaises(KeyError, obj.pop, 'Missing')
+        assert obj.pop('Missing', None) is None
+        assert obj.pop('Missing', default=None) is None
+        sentinel = object()
+        assert obj.pop('Missing', sentinel) is sentinel
+
+    def test_case_insensitive_update_invalid(self):
+        """Reject unsupported update sources with TypeError."""
+        obj = CaseInsensitiveDict()
+        self.assertRaises(TypeError, obj.update, 42)
+        assert not obj
+
     def test_case_insensitive_key(self):
         """Test the CaseInsensitiveKey class."""
         # Test the __eq__() special method.