diff --git a/ansible_mitogen/affinity.py b/ansible_mitogen/affinity.py
index 94539e21..eeeb4d38 100644
--- a/ansible_mitogen/affinity.py
+++ b/ansible_mitogen/affinity.py
@@ -142,7 +142,7 @@ class Policy(object):
         Assign the Ansible top-level policy to this process.
         """
 
-    def assign_muxprocess(self):
+    def assign_muxprocess(self, index):
         """
         Assign the MuxProcess policy to this process.
         """
@@ -224,7 +224,7 @@ class FixedPolicy(Policy):
         ))
 
     def _set_cpu(self, cpu):
-        self._set_affinity(1 << cpu)
+        self._set_affinity(1 << (cpu % self.cpu_count))
 
     def _clear(self):
         all_cpus = (1 << self.cpu_count) - 1
@@ -236,8 +236,8 @@ class FixedPolicy(Policy):
         else:
             self._balance()
 
-    def assign_muxprocess(self):
-        self._set_cpu(0)
+    def assign_muxprocess(self, index):
+        self._set_cpu(index)
 
     def assign_worker(self):
         self._balance()
diff --git a/ansible_mitogen/process.py b/ansible_mitogen/process.py
index 7cdd68ae..a8052061 100644
--- a/ansible_mitogen/process.py
+++ b/ansible_mitogen/process.py
@@ -586,7 +586,7 @@ class MuxProcess(object):
         """
         save_pid('mux')
         ansible_mitogen.logging.set_process_name('mux')
-        ansible_mitogen.affinity.policy.assign_muxprocess()
+        ansible_mitogen.affinity.policy.assign_muxprocess(self.index)
 
         self._setup_master()
         self._setup_services()