diff --git a/README.rst b/README.rst
index d7eb7a71..68b4406a 100644
--- a/README.rst
+++ b/README.rst
@@ -57,6 +57,8 @@ Install, configure and run
      # ctlplane_ssh_username = heat-admin
      # ctlplane_ssh_private_key_path = /home/stack/.ssh/id_rsa
      containers = true
+     max_compute_nodes = 2 # Some tests depend on there being a single
+                           # (available) compute node
 
 3. Execute the tests. ::
 
diff --git a/whitebox_tempest_plugin/api/compute/test_cpu_pinning.py b/whitebox_tempest_plugin/api/compute/test_cpu_pinning.py
index 95776b96..beb376dd 100644
--- a/whitebox_tempest_plugin/api/compute/test_cpu_pinning.py
+++ b/whitebox_tempest_plugin/api/compute/test_cpu_pinning.py
@@ -80,6 +80,8 @@ class CPUPolicyTest(BaseTest):
         flavor = self.create_flavor(cpu_policy='shared')
         self.create_test_server(flavor=flavor['id'])
 
+    @testtools.skipUnless(CONF.whitebox.max_compute_nodes < 2,
+                          'Single compute node required.')
     def test_cpu_dedicated(self):
         """Ensure an instance with 'dedicated' pinning policy work.
 
diff --git a/whitebox_tempest_plugin/config.py b/whitebox_tempest_plugin/config.py
index 56ca1192..57110e77 100644
--- a/whitebox_tempest_plugin/config.py
+++ b/whitebox_tempest_plugin/config.py
@@ -52,4 +52,9 @@ opts = [
              "While this looks like a poor man's DNS, this is needed "
              "because the environment running the test does not necessarily "
              "have the ctlplane DNS accessible."),
+    cfg.IntOpt(
+        'max_compute_nodes',
+        default=31337,
+        help="Number of compute hosts in the deployment. Some tests depend "
+             "on there being a single compute host."),
 ]