diff --git a/test/pylib/scylla_server.py b/test/pylib/scylla_server.py
diff --git a/test/pylib/util.py b/test/pylib/util.py
@@ -0,0 +1,20 @@
+#
+# Copyright (C) 2022-present ScyllaDB
+#
+# SPDX-License-Identifier: AGPL-3.0-or-later
+#
+import time
+
+unique_name_prefix = 'test_'
+
+
+def unique_name():
+    current_ms = int(round(time.time() * 1000))
+    # If unique_name() is called twice in the same millisecond...
+    if unique_name.last_ms >= current_ms:
+        current_ms = unique_name.last_ms + 1
+    unique_name.last_ms = current_ms
+    return unique_name_prefix + str(current_ms)
+
+
+unique_name.last_ms = 0
diff --git a/test/rest_api/suite.yaml b/test/rest_api/suite.yaml
@@ -1 +1,2 @@
-type: Run
+type: Python
+pool_size: 1
diff --git a/test/tools/cql_repl.cc b/test/tools/cql_repl.cc
diff --git a/test/topology/conftest.py b/test/topology/conftest.py
@@ -0,0 +1,15 @@
+#
+# Copyright (C) 2022-present ScyllaDB
+#
+# SPDX-License-Identifier: AGPL-3.0-or-later
+#
+# This file configures pytest for all tests in this directory, and also
+# defines common test fixtures for all of them to use
+
+import pathlib
+import sys
+
+# Add test.pylib to the search path
+sys.path.append(str(pathlib.Path(__file__).resolve().parents[1]))
+
+
diff --git a/test/topology/pytest.ini b/test/topology/pytest.ini
@@ -0,0 +1,6 @@
+# Pytest configuration file. If we don't have one in this directory,
+# pytest will look for one in our ancestor directories, and may find
+# something irrelevant. So we should have one here, even if empty.
+[pytest]
+# Use shared fixtures from the parent dir
+addopts = --confcutdir ..
diff --git a/test/topology/suite.yaml b/test/topology/suite.yaml
@@ -0,0 +1,7 @@
+type: Python
+pool_size: 4
+topology:
+    class: Simple
+    replication_factor: 3
+disable:
+    - test_null
diff --git a/test/topology/test_null.py b/test/topology/test_null.py
@@ -0,0 +1,26 @@
+#
+# Copyright (C) 2022-present ScyllaDB
+#
+# SPDX-License-Identifier: AGPL-3.0-or-later
+#
+from cassandra.protocol import InvalidRequest   # type: ignore
+from pylib.util import unique_name
+import pytest
+
+
+@pytest.fixture(scope="module")
+def table1(cql, test_keyspace):
+    table = test_keyspace + "." + unique_name()
+    cql.execute(f"CREATE TABLE {table} (p text, c text, v text, primary key (p, c))")
+    yield table
+    cql.execute("DROP TABLE " + table)
+
+
+def test_delete_empty_string_key(cql, table1):
+    s = "foobar"
+    # An empty-string clustering *is* allowed:
+    cql.execute(f"DELETE FROM {table1} WHERE p='{s}' AND c=''")
+    # But an empty-string partition key is *not* allowed, with a specific
+    # error that a "Key may not be empty":
+    with pytest.raises(InvalidRequest, match='Key may not be empty'):
+        cql.execute(f"DELETE FROM {table1} WHERE p='' AND c='{s}'")