diff --git a/spanner/tests/_fixtures.py b/spanner/tests/_fixtures.py
index fe7e038b8846..e7ce3e1865f5 100644
--- a/spanner/tests/_fixtures.py
+++ b/spanner/tests/_fixtures.py
@@ -47,6 +47,7 @@
     name STRING(16),
     tags ARRAY<STRING(16)> )
     PRIMARY KEY (id);
+CREATE INDEX name ON contacts(first_name, last_name);
 """
 
 DDL_STATEMENTS = [stmt.strip() for stmt in DDL.split(';') if stmt.strip()]
diff --git a/spanner/tests/system/test_system.py b/spanner/tests/system/test_system.py
index 1f8b7d1ddff9..a63c58233f9f 100644
--- a/spanner/tests/system/test_system.py
+++ b/spanner/tests/system/test_system.py
@@ -287,12 +287,12 @@ def test_update_database_ddl(self):
         self.to_delete.append(temp_db)
 
         # We want to make sure the operation completes.
-        create_op.result(90)  # raises on failure / timeout.
+        create_op.result(120)  # raises on failure / timeout.
 
         operation = temp_db.update_ddl(DDL_STATEMENTS)
 
         # We want to make sure the operation completes.
-        operation.result(90)  # raises on failure / timeout.
+        operation.result(120)  # raises on failure / timeout.
 
         temp_db.reload()
 
@@ -728,6 +728,22 @@ def _unit_of_work(transaction, test):
 
         return session, committed
 
+    def test_read_with_single_keys_index(self):
+        row_count = 10
+        columns = self.COLUMNS[1], self.COLUMNS[2]
+        session, committed = self._set_up_table(row_count)
+        self.to_delete.append(session)
+        expected = [[row[1], row[2]] for row in self._row_data(row_count)]
+        row = 5
+        keyset = [[expected[row][0], expected[row][1]]]
+        results_iter = session.read(self.TABLE,
+                                    columns,
+                                    KeySet(keys=keyset),
+                                    index='name'
+        )
+        rows = list(results_iter)
+        self.assertEqual(rows, [expected[row]])
+
     def test_snapshot_read_w_various_staleness(self):
         from datetime import datetime
         from google.cloud._helpers import UTC
@@ -815,7 +831,7 @@ def test_multiuse_snapshot_read_isolation_exact_staleness(self):
         self._check_row_data(after, all_data_rows)
 
     def test_read_w_manual_consume(self):
-        ROW_COUNT = 4000
+        ROW_COUNT = 3000
         session, committed = self._set_up_table(ROW_COUNT)
 
         snapshot = session.snapshot(read_timestamp=committed)
@@ -888,7 +904,7 @@ def test_read_w_multiple_keys(self):
         self._check_row_data(rows, expected)
 
     def test_read_w_limit(self):
-        ROW_COUNT = 4000
+        ROW_COUNT = 3000
         LIMIT = 100
         session, committed = self._set_up_table(ROW_COUNT)
 
@@ -901,7 +917,7 @@ def test_read_w_limit(self):
         self._check_row_data(rows, expected)
 
     def test_read_w_ranges(self):
-        ROW_COUNT = 4000
+        ROW_COUNT = 3000
         START = 1000
         END = 2000
         session, committed = self._set_up_table(ROW_COUNT)
@@ -937,7 +953,7 @@ def test_read_w_ranges(self):
         self._check_row_data(rows, expected)
 
     def test_execute_sql_w_manual_consume(self):
-        ROW_COUNT = 4000
+        ROW_COUNT = 3000
         session, committed = self._set_up_table(ROW_COUNT)
 
         snapshot = session.snapshot(read_timestamp=committed)