diff --git a/tests/backends/tests.py b/tests/backends/tests.py
index f5ec488c86..fc62c6587c 100644
--- a/tests/backends/tests.py
+++ b/tests/backends/tests.py
@@ -370,10 +370,7 @@ class LastExecutedQueryTest(TestCase):
         query has been run.
         """
         cursor = connection.cursor()
-        try:
-            connection.ops.last_executed_query(cursor, '', ())
-        except Exception:
-            self.fail("'last_executed_query' should not raise an exception.")
+        connection.ops.last_executed_query(cursor, '', ())
 
     def test_debug_sql(self):
         list(models.Reporter.objects.filter(first_name="test"))
diff --git a/tests/files/tests.py b/tests/files/tests.py
index 13560e509c..cd2ccaf9f1 100644
--- a/tests/files/tests.py
+++ b/tests/files/tests.py
@@ -6,7 +6,6 @@ import os
 import struct
 import tempfile
 import unittest
-import zlib
 from io import BytesIO, StringIO
 
 from django.core.files import File
@@ -233,10 +232,7 @@ class InconsistentGetImageDimensionsBug(unittest.TestCase):
         get_image_dimensions fails on some pngs, while Image.size is working good on them
         """
         img_path = os.path.join(os.path.dirname(upath(__file__)), "magic.png")
-        try:
-            size = images.get_image_dimensions(img_path)
-        except zlib.error:
-            self.fail("Exception raised from get_image_dimensions().")
+        size = images.get_image_dimensions(img_path)
         with open(img_path, 'rb') as fh:
             self.assertEqual(size, Image.open(fh).size)
 
diff --git a/tests/gis_tests/layermap/tests.py b/tests/gis_tests/layermap/tests.py
index a0abd4030c..3ebbf4292e 100644
--- a/tests/gis_tests/layermap/tests.py
+++ b/tests/gis_tests/layermap/tests.py
@@ -140,19 +140,19 @@ class LayerMapTest(TestCase):
     def test_layermap_unique_multigeometry_fk(self):
         "Testing the `unique`, and `transform`, geometry collection conversion, and ForeignKey mappings."
         # All the following should work.
-        try:
-            # Telling LayerMapping that we want no transformations performed on the data.
-            lm = LayerMapping(County, co_shp, co_mapping, transform=False)
 
-            # Specifying the source spatial reference system via the `source_srs` keyword.
-            lm = LayerMapping(County, co_shp, co_mapping, source_srs=4269)
-            lm = LayerMapping(County, co_shp, co_mapping, source_srs='NAD83')
+        # Telling LayerMapping that we want no transformations performed on the data.
+        lm = LayerMapping(County, co_shp, co_mapping, transform=False)
 
-            # Unique may take tuple or string parameters.
-            for arg in ('name', ('name', 'mpoly')):
-                lm = LayerMapping(County, co_shp, co_mapping, transform=False, unique=arg)
-        except Exception:
-            self.fail('No exception should be raised for proper use of keywords.')
+        # Specifying the source spatial reference system via the `source_srs` keyword.
+        lm = LayerMapping(County, co_shp, co_mapping, source_srs=4269)
+        lm = LayerMapping(County, co_shp, co_mapping, source_srs='NAD83')
+
+        # Unique may take tuple or string parameters.
+        for arg in ('name', ('name', 'mpoly')):
+            lm = LayerMapping(County, co_shp, co_mapping, transform=False, unique=arg)
+
+        # Now test for failures
 
         # Testing invalid params for the `unique` keyword.
         for e, arg in ((TypeError, 5.0), (ValueError, 'foobar'), (ValueError, ('name', 'mpolygon'))):
diff --git a/tests/mail/tests.py b/tests/mail/tests.py
index 03dfae7903..f6eff3bb8f 100644
--- a/tests/mail/tests.py
+++ b/tests/mail/tests.py
@@ -695,10 +695,7 @@ class BaseEmailBackendTests(HeadersCheckMixin, object):
         Test that connection can be closed (even when not explicitly opened)
         """
         conn = mail.get_connection(username='', password='')
-        try:
-            conn.close()
-        except Exception as e:
-            self.fail("close() unexpectedly raised an exception: %s" % e)
+        conn.close()
 
     def test_use_as_contextmanager(self):
         """
@@ -1146,7 +1143,4 @@ class SMTPBackendStoppedServerTest(SMTPBackendTestsBase):
         backend = smtp.EmailBackend(username='', password='')
         backend.open()
         self.server.stop()
-        try:
-            backend.close()
-        except Exception as e:
-            self.fail("close() unexpectedly raised an exception: %s" % e)
+        backend.close()