diff --git a/tests/modeltests/one_to_one/models.py b/tests/modeltests/one_to_one/models.py
index ab478c6118..e7b2668a85 100644
--- a/tests/modeltests/one_to_one/models.py
+++ b/tests/modeltests/one_to_one/models.py
@@ -6,7 +6,7 @@ To define a one-to-one relationship, use ``OneToOneField()``.
 In this example, a ``Place`` optionally can be a ``Restaurant``.
 """
 
-from django.db import models
+from django.db import models, connection
 
 class Place(models.Model):
     name = models.CharField(max_length=50)
@@ -185,4 +185,9 @@ DoesNotExist: Restaurant matching query does not exist.
 Traceback (most recent call last):
     ...
 IntegrityError: ...
+
+# Because the unittests all use a single connection, we need to force a
+# reconnect here to ensure the connection is clean (after the previous
+# IntegrityError).
+>>> connection.close()
 """}
diff --git a/tests/regressiontests/queries/models.py b/tests/regressiontests/queries/models.py
index 50c002d14d..ada5f1cfc3 100644
--- a/tests/regressiontests/queries/models.py
+++ b/tests/regressiontests/queries/models.py
@@ -537,6 +537,10 @@ Test that parallel iterators work.
 
 We can do slicing beyond what is currently in the result cache, too.
 
+# FIXME!! This next test causes really weird PostgreSQL behaviour, but it's
+# only apparent much later when the full test suite runs. I don't understand
+# what's going on here yet.
+
 # We need to mess with the implemenation internals a bit here to decrease the
 # cache fill size so that we don't read all the results at once.
 >>> from django.db.models import query