diff --git a/django/db/backends/mysql/introspection.py b/django/db/backends/mysql/introspection.py
index 93e89c1263..477478ca9d 100644
--- a/django/db/backends/mysql/introspection.py
+++ b/django/db/backends/mysql/introspection.py
@@ -103,6 +103,7 @@ class DatabaseIntrospection(BaseDatabaseIntrospection):
                 continue
             if row[4] not in indexes:
                 indexes[row[4]] = {'primary_key': False, 'unique': False}
+            # It's possible to have the unique and PK constraints in separate indexes.
             if row[2] == 'PRIMARY':
                 indexes[row[4]]['primary_key'] = True
             if not bool(row[1]):
diff --git a/django/db/backends/postgresql_psycopg2/introspection.py b/django/db/backends/postgresql_psycopg2/introspection.py
index 5a29932859..d43b95406c 100644
--- a/django/db/backends/postgresql_psycopg2/introspection.py
+++ b/django/db/backends/postgresql_psycopg2/introspection.py
@@ -86,7 +86,13 @@ class DatabaseIntrospection(BaseDatabaseIntrospection):
             # Here, we skip any indexes across multiple fields.
             if ' ' in row[1]:
                 continue
-            indexes[row[0]] = {'primary_key': row[3], 'unique': row[2]}
+            if row[0] not in indexes:
+                indexes[row[0]] = {'primary_key': False, 'unique': False}
+            # It's possible to have the unique and PK constraints in separate indexes.
+            if row[3]:
+                indexes[row[0]]['primary_key'] = True
+            if row[2]:
+                indexes[row[0]]['unique'] = True
         return indexes
 
     def get_constraints(self, cursor, table_name):