diff --git a/superset/connectors/sqla/models.py b/superset/connectors/sqla/models.py
index ad45474c33b35..84b2ffe0104c7 100644
--- a/superset/connectors/sqla/models.py
+++ b/superset/connectors/sqla/models.py
@@ -373,7 +373,11 @@ class SqlaTable(Model, BaseDatasource):
     owner_class = security_manager.user_model
 
     __tablename__ = "tables"
-    __table_args__ = (UniqueConstraint("database_id", "table_name"),)
+    __table_args__ = (
+        UniqueConstraint(
+            "database_id", "schema", "table_name", name="_customer_location_uc",
+        ),
+    )
 
     table_name = Column(String(250), nullable=False)
     main_dttm_col = Column(String(250))
diff --git a/superset/migrations/versions/4e6a06bad7a8_init.py b/superset/migrations/versions/4e6a06bad7a8_init.py
index 31d46b8798ff3..a6956805433ca 100644
--- a/superset/migrations/versions/4e6a06bad7a8_init.py
+++ b/superset/migrations/versions/4e6a06bad7a8_init.py
@@ -127,7 +127,9 @@ def upgrade():
             "changed_by_fk", sa.Integer(), sa.ForeignKey("ab_user.id"), nullable=True
         ),
         sa.PrimaryKeyConstraint("id"),
-        sa.UniqueConstraint("table_name"),
+        # Commenting out spring 2020 to avoid flimsy delete in
+        # subsequent migration b4456560d4f3_change_table_unique_constraint.py
+        # sa.UniqueConstraint("table_name"),
     )
     op.create_table(
         "columns",
diff --git a/superset/migrations/versions/b4456560d4f3_change_table_unique_constraint.py b/superset/migrations/versions/b4456560d4f3_change_table_unique_constraint.py
index d22f72cf03c7d..72d08e71091c7 100644
--- a/superset/migrations/versions/b4456560d4f3_change_table_unique_constraint.py
+++ b/superset/migrations/versions/b4456560d4f3_change_table_unique_constraint.py
@@ -27,21 +27,24 @@
 revision = "b4456560d4f3"
 down_revision = "bb51420eaf83"
 
+conv = {
+    "uq": "uq_%(table_name)s_%(column_0_name)s",
+}
+
 
 def upgrade():
     try:
-        # Trying since sqlite doesn't like constraints
-        op.drop_constraint("tables_table_name_key", "tables", type_="unique")
-        op.create_unique_constraint(
-            "_customer_location_uc", "tables", ["database_id", "schema", "table_name"]
-        )
+        with op.get_context().autocommit_block():
+            with op.batch_alter_table("tables", naming_convention=conv) as batch_op:
+                # Trying to drop the constraint if it exists
+                batch_op.drop_constraint("tables_table_name_key", type_="unique")
     except Exception:
         pass
+    with op.batch_alter_table("tables", naming_convention=conv) as batch_op:
+        batch_op.create_unique_constraint(
+            "_customer_location_uc", ["database_id", "schema", "table_name"],
+        )
 
 
 def downgrade():
-    try:
-        # Trying since sqlite doesn't like constraints
-        op.drop_constraint(u"_customer_location_uc", "tables", type_="unique")
-    except Exception:
-        pass
+    op.drop_constraint("_customer_location_uc", "tables", type_="unique")