diff --git a/ansible_mitogen/connection.py b/ansible_mitogen/connection.py
index 5053a5f5b..669587a11 100644
--- a/ansible_mitogen/connection.py
+++ b/ansible_mitogen/connection.py
@@ -422,7 +422,9 @@ def _connect_mitogen_doas(spec):
     'ssh': _connect_ssh,
     'smart': _connect_ssh,  # issue #548.
     'su': _connect_su,
+    'ansible.builtin.su': _connect_su,
     'sudo': _connect_sudo,
+    'ansible.builtin.sudo': _connect_sudo,
     'doas': _connect_doas,
     'mitogen_su': _connect_mitogen_su,
     'mitogen_sudo': _connect_mitogen_sudo,
diff --git a/docs/changelog.rst b/docs/changelog.rst
index 16f082f79..c2e5f84f1 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -21,6 +21,8 @@ To avail of fixes in an unreleased version, please download a ZIP file
 In progress (unreleased)
 ------------------------
 
+* :gh:issue:`1232` :mod:`ansible_mitogen`: Add support for fully qualified
+  connection names in become_method
 * :gh:issue:`1213` tests: Enable default Python warnings
 * :gh:issue:`1111` :mod:`mitogen`: Replace uses of deprecated
   :py:func:`pkgutil.find_loader`
diff --git a/tests/ansible/regression/all.yml b/tests/ansible/regression/all.yml
index 70b5ffe77..c14225a0a 100644
--- a/tests/ansible/regression/all.yml
+++ b/tests/ansible/regression/all.yml
@@ -19,3 +19,4 @@
 - import_playbook: issue_1066__add_host__host_key_checking.yml
 - import_playbook: issue_1079__wait_for_connection_timeout.yml
 - import_playbook: issue_1087__template_streamerror.yml
+- import_playbook: issue_1232__fully_qualified_names_become_method.yml
diff --git a/tests/ansible/regression/issue_1232__fully_qualified_names_become_method.yml b/tests/ansible/regression/issue_1232__fully_qualified_names_become_method.yml
new file mode 100644
index 000000000..390084ce4
--- /dev/null
+++ b/tests/ansible/regression/issue_1232__fully_qualified_names_become_method.yml
@@ -0,0 +1,23 @@
+- name: regression/issue_1232__fully_qualified_names_become_method.yml (1/2)
+  hosts: test-targets
+  become_method: ansible.builtin.sudo
+  tasks:
+    - name: Run a shell command with sudo root
+      vars:
+        ansible_become_pass: rootpassword
+      ansible.builtin.command: whoami
+      become: true
+      become_user: root
+
+- name: regression/issue_1232__fully_qualified_names_become_method.yml (2/2)
+  hosts: test-targets
+  become_method: ansible.builtin.su
+  tasks:
+    - name: Run a shell command with su mitogen__user1
+      vars:
+        ansible_become_pass: user1_password
+      when:
+        - become_unpriv_available
+      ansible.builtin.command: whoami
+      become: true
+      become_user: mitogen__user1