diff --git a/Lib/test/test_hashlib.py b/Lib/test/test_hashlib.py
index e6365c5..dac945c 100644
--- a/Lib/test/test_hashlib.py
+++ b/Lib/test/test_hashlib.py
@@ -207,30 +207,20 @@
         self.check('md5', 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789',
                    'd174ab98d277d9f5a5611c2c9f419d9f')
 
-    @precisionbigmemtest(size=_4G + 5, memuse=1)
+    @unittest.skipIf(sys.maxsize < _4G + 5, 'test cannot run on 32-bit systems')
+    @precisionbigmemtest(size=_4G + 5, memuse=1, dry_run=False)
     def test_case_md5_huge(self, size):
-        if size == _4G + 5:
-            try:
-                self.check('md5', 'A'*size, 'c9af2dff37468ce5dfee8f2cfc0a9c6d')
-            except OverflowError:
-                pass # 32-bit arch
+        self.check('md5', 'A'*size, 'c9af2dff37468ce5dfee8f2cfc0a9c6d')
 
-    @precisionbigmemtest(size=_4G + 5, memuse=1)
+    @unittest.skipIf(sys.maxsize < _4G + 5, 'test cannot run on 32-bit systems')
+    @precisionbigmemtest(size=_4G + 5, memuse=1, dry_run=False)
     def test_case_md5_huge_update(self, size):
-        if size == _4G + 5:
-            try:
-                self.check_update('md5', 'A'*size,
-                        'c9af2dff37468ce5dfee8f2cfc0a9c6d')
-            except OverflowError:
-                pass # 32-bit arch
+        self.check_update('md5', 'A'*size, 'c9af2dff37468ce5dfee8f2cfc0a9c6d')
 
-    @precisionbigmemtest(size=_4G - 1, memuse=1)
+    @unittest.skipIf(sys.maxsize < _4G - 1, 'test cannot run on 32-bit systems')
+    @precisionbigmemtest(size=_4G - 1, memuse=1, dry_run=False)
     def test_case_md5_uintmax(self, size):
-        if size == _4G - 1:
-            try:
-                self.check('md5', 'A'*size, '28138d306ff1b8281f1a9067e1a1a2b3')
-            except OverflowError:
-                pass # 32-bit arch
+        self.check('md5', 'A'*size, '28138d306ff1b8281f1a9067e1a1a2b3')
 
     # use the three examples from Federal Information Processing Standards
     # Publication 180-1, Secure Hash Standard,  1995 April 17
diff --git a/Lib/test/test_marshal.py b/Lib/test/test_marshal.py
index bbe8eac..f7cd195 100644
--- a/Lib/test/test_marshal.py
+++ b/Lib/test/test_marshal.py
@@ -286,7 +286,7 @@
         self.check_unmarshallable('x' * size)
 
     @test_support.precisionbigmemtest(size=LARGE_SIZE,
-            memuse=character_size, dry_run=False)
+            memuse=character_size + 2, dry_run=False)
     def test_unicode(self, size):
         self.check_unmarshallable(u'x' * size)