diff --git a/django/db/backends/postgresql_psycopg2/creation.py b/django/db/backends/postgresql_psycopg2/creation.py
index ca389b9046..90304aa566 100644
--- a/django/db/backends/postgresql_psycopg2/creation.py
+++ b/django/db/backends/postgresql_psycopg2/creation.py
@@ -41,7 +41,8 @@ class DatabaseCreation(BaseDatabaseCreation):
         return ''
 
     def sql_indexes_for_field(self, model, f, style):
-        if f.db_index and not f.unique:
+        output = []
+        if f.db_index:
             qn = self.connection.ops.quote_name
             db_table = model._meta.db_table
             tablespace = f.db_tablespace or model._meta.db_tablespace
@@ -60,7 +61,8 @@ class DatabaseCreation(BaseDatabaseCreation):
                         "(%s%s)" % (style.SQL_FIELD(qn(f.column)), opclass) +
                         "%s;" % tablespace_sql)
 
-            output = [get_index_sql('%s_%s' % (db_table, f.column))]
+            if not f.unique:
+                output = [get_index_sql('%s_%s' % (db_table, f.column))]
 
             # Fields with database column types of `varchar` and `text` need
             # a second index that specifies their operator class, which is
@@ -73,8 +75,6 @@ class DatabaseCreation(BaseDatabaseCreation):
             elif db_type.startswith('text'):
                 output.append(get_index_sql('%s_%s_like' % (db_table, f.column),
                                             ' text_pattern_ops'))
-        else:
-            output = []
         return output
 
     def set_autocommit(self):
diff --git a/tests/regressiontests/indexes/models.py b/tests/regressiontests/indexes/models.py
index 9758377f99..47ba5896a8 100644
--- a/tests/regressiontests/indexes/models.py
+++ b/tests/regressiontests/indexes/models.py
@@ -9,3 +9,9 @@ class Article(models.Model):
         index_together = [
             ["headline", "pub_date"],
         ]
+
+
+class IndexedArticle(models.Model):
+    headline = models.CharField(max_length=100, db_index=True)
+    body = models.TextField(db_index=True)
+    slug = models.CharField(max_length=40, unique=True, db_index=True)
diff --git a/tests/regressiontests/indexes/tests.py b/tests/regressiontests/indexes/tests.py
index 0dac881fa9..f3a32a44bb 100644
--- a/tests/regressiontests/indexes/tests.py
+++ b/tests/regressiontests/indexes/tests.py
@@ -1,8 +1,9 @@
 from django.core.management.color import no_style
 from django.db import connections, DEFAULT_DB_ALIAS
 from django.test import TestCase
+from django.utils.unittest import skipUnless
 
-from .models import Article
+from .models import Article, IndexedArticle
 
 
 class IndexesTests(TestCase):
@@ -10,3 +11,16 @@ class IndexesTests(TestCase):
         connection = connections[DEFAULT_DB_ALIAS]
         index_sql = connection.creation.sql_indexes_for_model(Article, no_style())
         self.assertEqual(len(index_sql), 1)
+
+    @skipUnless(connections[DEFAULT_DB_ALIAS].vendor == 'postgresql',
+        "This is a postgresql-specific issue")
+    def test_postgresql_text_indexes(self):
+        """Test creation of PostgreSQL-specific text indexes (#12234)"""
+        connection = connections[DEFAULT_DB_ALIAS]
+        index_sql = connection.creation.sql_indexes_for_model(IndexedArticle, no_style())
+        self.assertEqual(len(index_sql), 5)
+        self.assertIn('("headline" varchar_pattern_ops)', index_sql[1])
+        self.assertIn('("body" text_pattern_ops)', index_sql[3])
+        # unique=True and db_index=True should only create the varchar-specific
+        # index (#19441).
+        self.assertIn('("slug" varchar_pattern_ops)', index_sql[4])