diff --git a/run-tests.py b/run-tests.py
index b956773380..82b097cb91 100755
--- a/run-tests.py
+++ b/run-tests.py
@@ -12,7 +12,6 @@
 import argparse
 import subprocess
 import pytest
-import unittest
 
 
 def run_code_tests(executable=False, folder: str = "unit", interpreter="python"):
@@ -37,18 +36,10 @@ def run_code_tests(executable=False, folder: str = "unit", interpreter="python")
         # currently activated virtual environment
         interpreter = sys.executable
     if executable is False:
-        if tests == "tests/unit":
-            ret = pytest.main(["-v", tests])
-        else:
-            suite = unittest.defaultTestLoader.discover(tests, pattern="test*.py")
-            result = unittest.TextTestRunner(verbosity=2).run(suite)
-            ret = int(not result.wasSuccessful())
+        ret = pytest.main(["-v", tests])
     else:
         print(f"Running {folder} tests with executable {interpreter}")
-        if tests == "tests/unit":
-            cmd = [interpreter, "-m", "pytest", "-v", tests]
-        else:
-            cmd = [interpreter, "-m", "unittest", "discover", "-v", tests]
+        cmd = [interpreter, "-m", "pytest", "-v", tests]
         p = subprocess.Popen(cmd)
         try:
             ret = p.wait()
diff --git a/tests/integration/test_models/standard_model_tests.py b/tests/integration/test_models/standard_model_tests.py
index ac06f95c9f..7f0e9e6137 100644
--- a/tests/integration/test_models/standard_model_tests.py
+++ b/tests/integration/test_models/standard_model_tests.py
@@ -3,6 +3,7 @@
 #
 import pybamm
 import tests
+import uuid
 
 import numpy as np
 import os
@@ -140,11 +141,14 @@ def test_sensitivities(self, param_name, param_value, output_name="Voltage [V]")
         )
 
     def test_serialisation(self, solver=None, t_eval=None):
+        # Generating unique file names to avoid race conditions when run in parallel.
+        unique_id = uuid.uuid4()
+        file_name = f"test_model_{unique_id}"
         self.model.save_model(
-            "test_model", variables=self.model.variables, mesh=self.disc.mesh
+            file_name, variables=self.model.variables, mesh=self.disc.mesh
         )
 
-        new_model = pybamm.load_model("test_model.json")
+        new_model = pybamm.load_model(file_name + ".json")
 
         # create new solver for re-created model
         if solver is not None:
@@ -175,7 +179,7 @@ def test_serialisation(self, solver=None, t_eval=None):
                 new_solution.all_ys[x], self.solution.all_ys[x], decimal=accuracy
             )
 
-        os.remove("test_model.json")
+        os.remove(file_name + ".json")
 
     def test_all(
         self, param=None, disc=None, solver=None, t_eval=None, skip_output_tests=False