diff -r 5e0f9b8e6c2b Lib/tkinter/test/test_tkinter/test_widgets.py
--- a/Lib/tkinter/test/test_tkinter/test_widgets.py	Sat Feb 01 23:14:59 2014 -0500
+++ b/Lib/tkinter/test/test_tkinter/test_widgets.py	Sun Feb 02 22:33:11 2014 +0200
@@ -329,10 +329,11 @@
         self.checkColorParam(widget, 'disabledbackground')
 
     def test_insertborderwidth(self):
-        widget = self.create()
-        self.checkPixelsParam(widget, 'insertborderwidth', 0, 1.3, -2)
-        self.checkParam(widget, 'insertborderwidth', 2, expected=1)
-        self.checkParam(widget, 'insertborderwidth', '10p', expected=1)
+        widget = self.create(insertwidth=100)
+        self.checkPixelsParam(widget, 'insertborderwidth',
+                              0, 1.3, 2.6, 6, -2, '10p')
+        # insertborderwidth is bounded above by a half of insertwidth.
+        self.checkParam(widget, 'insertborderwidth', 60, expected=100//2)
 
     def test_insertwidth(self):
         widget = self.create()
diff -r 5e0f9b8e6c2b Lib/tkinter/test/widget_tests.py
--- a/Lib/tkinter/test/widget_tests.py	Sat Feb 01 23:14:59 2014 -0500
+++ b/Lib/tkinter/test/widget_tests.py	Sun Feb 02 22:33:11 2014 +0200
@@ -6,6 +6,7 @@
 from tkinter.ttk import setup_master, Scale
 from tkinter.test.support import (tcl_version, requires_tcl, get_tk_patchlevel,
                                   pixels_conv, tcl_obj_eq)
+import test.support
 
 
 noconv = False
@@ -234,8 +235,14 @@
         widget = self.create()
         self.checkParam(widget, 'bitmap', 'questhead')
         self.checkParam(widget, 'bitmap', 'gray50')
-        self.checkInvalidParam(widget, 'bitmap', 'spam',
-                errmsg='bitmap "spam" not defined')
+        filename = test.support.findfile('python.xbm', subdir='imghdrdata')
+        self.checkParam(widget, 'bitmap', '@' + filename)
+        # Cocoa Tk widgets don't detect invalid -bitmap values
+        # See https://core.tcl.tk/tk/info/31cd33dbf0
+        if not ('aqua' in self.root.tk.call('tk', 'windowingsystem') and
+                'AppKit' in self.root.winfo_server()):
+            self.checkInvalidParam(widget, 'bitmap', 'spam',
+                    errmsg='bitmap "spam" not defined')
 
     def test_borderwidth(self):
         widget = self.create()
@@ -495,7 +502,6 @@
     return decorator
 
 def setUpModule():
-    import test.support
     if test.support.verbose:
         tcl = tkinter.Tcl()
         print('patchlevel =', tcl.call('info', 'patchlevel'))