diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index 46810ff5064..09d204ecb0a 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -1081,14 +1081,14 @@ def test_install_package_conflict_prefix_and_user(script, data):
     )
 
 
-def test_install_package_that_emits_unicode(script, data):
+def test_install_package_that_emits_unicode(script_no_wheel, data):
     """
     Install a package with a setup.py that emits UTF-8 output and then fails.
 
     Refs https://github.com/pypa/pip/issues/326
     """
     to_install = data.packages.joinpath("BrokenEmitsUTF8")
-    result = script.pip(
+    result = script_no_wheel.pip(
         'install', to_install, expect_error=True, expect_temp=True, quiet=True,
     )
     assert (
@@ -1648,17 +1648,22 @@ def test_installing_scripts_on_path_does_not_print_warning(script):
     assert "--no-warn-script-location" not in result.stderr
 
 
-def test_installed_files_recorded_in_deterministic_order(script, data):
+def test_installed_files_recorded_in_deterministic_order(
+    script_no_wheel, data
+):
     """
     Ensure that we record the files installed by a package in a deterministic
     order, to make installs reproducible.
     """
     to_install = data.packages.joinpath("FSPkg")
-    result = script.pip('install', to_install)
-    fspkg_folder = script.site_packages / 'fspkg'
+    # allow_stderr_warning for https://github.com/pypa/pip/issues/8559
+    result = script_no_wheel.pip(
+        'install', to_install, allow_stderr_warning=True
+    )
+    fspkg_folder = script_no_wheel.site_packages / 'fspkg'
     egg_info = 'FSPkg-0.1.dev0-py{pyversion}.egg-info'.format(**globals())
     installed_files_path = (
-        script.site_packages / egg_info / 'installed-files.txt'
+        script_no_wheel.site_packages / egg_info / 'installed-files.txt'
     )
     result.did_create(fspkg_folder)
     result.did_create(installed_files_path)
diff --git a/tests/functional/test_install_compat.py b/tests/functional/test_install_compat.py
index a5a0df65218..202426d3037 100644
--- a/tests/functional/test_install_compat.py
+++ b/tests/functional/test_install_compat.py
@@ -11,7 +11,7 @@
 
 
 @pytest.mark.network
-def test_debian_egg_name_workaround(script):
+def test_debian_egg_name_workaround(script_no_wheel):
     """
     We can uninstall packages installed with the pyversion removed from the
     egg-info metadata directory name.
@@ -22,10 +22,13 @@ def test_debian_egg_name_workaround(script):
     https://bitbucket.org/ianb/pip/issue/104/pip-uninstall-on-ubuntu-linux
 
     """
-    result = script.pip('install', 'INITools==0.2')
+    # allow_stderr_warning for https://github.com/pypa/pip/issues/8559
+    result = script_no_wheel.pip(
+        'install', 'INITools==0.2', allow_stderr_warning=True
+    )
 
     egg_info = os.path.join(
-        script.site_packages,
+        script_no_wheel.site_packages,
         "INITools-0.2-py{pyversion}.egg-info".format(**globals()))
 
     # Debian only removes pyversion for global installs, not inside a venv
@@ -38,22 +41,26 @@ def test_debian_egg_name_workaround(script):
     )
 
     # The Debian no-pyversion version of the .egg-info
-    mangled = os.path.join(script.site_packages, "INITools-0.2.egg-info")
+    mangled = os.path.join(
+        script_no_wheel.site_packages, "INITools-0.2.egg-info"
+    )
     result.did_not_create(
         mangled,
         message="Found unexpected {mangled}".format(**locals())
     )
 
     # Simulate a Debian install by copying the .egg-info to their name for it
-    full_egg_info = os.path.join(script.base_path, egg_info)
+    full_egg_info = os.path.join(script_no_wheel.base_path, egg_info)
     assert os.path.isdir(full_egg_info)
-    full_mangled = os.path.join(script.base_path, mangled)
+    full_mangled = os.path.join(script_no_wheel.base_path, mangled)
     os.renames(full_egg_info, full_mangled)
     assert os.path.isdir(full_mangled)
 
     # Try the uninstall and verify that everything is removed.
-    result2 = script.pip("uninstall", "INITools", "-y")
-    assert_all_changes(result, result2, [script.venv / 'build', 'cache'])
+    result2 = script_no_wheel.pip("uninstall", "INITools", "-y")
+    assert_all_changes(
+        result, result2, [script_no_wheel.venv / 'build', 'cache']
+    )
 
 
 def test_setup_py_with_dos_line_endings(script, data):