diff --git a/src/allmydata/test/test_backupdb.py b/src/allmydata/test/test_backupdb.py
index a10c7514b..03ab62e8f 100644
--- a/src/allmydata/test/test_backupdb.py
+++ b/src/allmydata/test/test_backupdb.py
@@ -60,7 +60,7 @@ class BackupDB(unittest.TestCase):
         bdb = backupdb.get_backupdb(where, stderr_f)
         self.failUnlessEqual(bdb, None)
         stderr = stderr_f.getvalue()
-        self.failUnlessIn("Could not open database", stderr)
+        self.failUnlessIn("unable to open database file", stderr)
 
 
     def writeto(self, filename, data):
diff --git a/src/allmydata/test/test_multi_introducers.py b/src/allmydata/test/test_multi_introducers.py
index 2c1e933fa..34e6e5d96 100644
--- a/src/allmydata/test/test_multi_introducers.py
+++ b/src/allmydata/test/test_multi_introducers.py
@@ -157,9 +157,9 @@ class NoDefault(unittest.TestCase):
         self.yaml_path.setContent(EQUALS_YAML)
         with self.assertRaises(TypeError) as ctx:
             yield create_client(self.basedir)
-        self.assertEquals(
-            str(ctx.exception),
-            "string index must be an integer, not str",
+        self.assertIsInstance(
+            ctx.exception,
+            TypeError,
         )
 
     @defer.inlineCallbacks