diff --git a/doc/source/release.rst b/doc/source/release.rst
index 5db612059685b..5b6a0d15be943 100644
--- a/doc/source/release.rst
+++ b/doc/source/release.rst
@@ -317,10 +317,11 @@ API Changes
   - Arithemtic func factories are now passed real names (suitable for using with super) (:issue:`5240`)
   - Provide numpy compatibility with 1.7 for a calling convention like ``np.prod(pandas_object)`` as numpy
     call with additional keyword args (:issue:`4435`)
-  - Provide __dir__ method (and local context) for tab completion / remove ipython completers code
-    (:issue:`4501`)
+  - Provide ``__dir__`` method (and local context) for tab completion / remove
+    ipython completers code (:issue:`4501`)
   - Support non-unique axes in a Panel via indexing operations (:issue:`4960`)
   - ``.truncate`` will raise a ``ValueError`` if invalid before and afters dates are given (:issue:`5242`)
+  - Improve some exceptions in core/generic. (:issue:`5051`)
 
 Internal Refactoring
 ~~~~~~~~~~~~~~~~~~~~
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 9666fe42cc822..100c546753154 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -233,8 +233,8 @@ def _construct_axes_from_arguments(self, args, kwargs, require_all=False):
             if alias is not None:
                 if a in kwargs:
                     if alias in kwargs:
-                        raise Exception(
-                            "arguments are multually exclusive for [%s,%s]" % (a, alias))
+                        raise TypeError("arguments are multually exclusive "
+                                         "for [%s,%s]" % (a, alias))
                     continue
                 if alias in kwargs:
                     kwargs[a] = kwargs.pop(alias)
@@ -244,10 +244,9 @@ def _construct_axes_from_arguments(self, args, kwargs, require_all=False):
             if a not in kwargs:
                 try:
                     kwargs[a] = args.pop(0)
-                except (IndexError):
+                except IndexError:
                     if require_all:
-                        raise AssertionError(
-                            "not enough arguments specified!")
+                        raise TypeError("not enough arguments specified!")
 
         axes = dict([(a, kwargs.get(a)) for a in self._AXIS_ORDERS])
         return axes, kwargs
@@ -273,7 +272,8 @@ def _get_axis_number(self, axis):
                 return self._AXIS_NUMBERS[axis]
             except:
                 pass
-        raise ValueError('No axis named {0} for object type {1}'.format(axis,type(self)))
+        raise ValueError('No axis named {0} for object type {1}'.format(
+                          axis, type(self).__name__))
 
     def _get_axis_name(self, axis):
         axis = self._AXIS_ALIASES.get(axis, axis)
@@ -285,7 +285,8 @@ def _get_axis_name(self, axis):
                 return self._AXIS_NAMES[axis]
             except:
                 pass
-        raise ValueError('No axis named {0} for object type {1}'.format(axis,type(self)))
+        raise ValueError('No axis named {0} for object type {1}'.format(
+                          axis, type(self).__name__))
 
     def _get_axis(self, axis):
         name = self._get_axis_name(axis)
diff --git a/pandas/tests/test_panel.py b/pandas/tests/test_panel.py
index 07b33266d88a1..7b5e6ac2dd1cf 100644
--- a/pandas/tests/test_panel.py
+++ b/pandas/tests/test_panel.py
@@ -1250,12 +1250,19 @@ def test_transpose(self):
 
         ## test bad aliases
         # test ambiguous aliases
-        self.assertRaises(AssertionError, self.panel.transpose, 'minor',
-                          maj='major', majo='items')
+        with tm.assertRaisesRegexp(TypeError, 'not enough arguments'):
+            self.panel.transpose('minor', maj='major', majo='items')
 
         # test invalid kwargs
-        self.assertRaises(AssertionError, self.panel.transpose, 'minor',
-                          maj='major', minor='items')
+        # TODO: Decide whether to remove this test - it's no longer testing
+        #       the correct thing on current master (and hasn't been for a
+        #       while)
+        with tm.assertRaisesRegexp(TypeError, 'not enough arguments'):
+            self.panel.transpose('minor', maj='major', minor='items')
+
+        # does this test make sense?
+        # with tm.assertRaisesRegexp(ValueError, 'duplicate axes'):
+        #     self.panel.transpose('minor', 'major', major='minor', minor='items')
 
         result = self.panel.transpose(2, 1, 0)
         assert_panel_equal(result, expected)