diff --git a/vinca/main.py b/vinca/main.py
index 8aa17e2..96d210a 100644
--- a/vinca/main.py
+++ b/vinca/main.py
@@ -341,6 +341,16 @@ def conda_index_shadowed_packages(distro, vinca_conf):
     return names
 
 
+def expected_build_number(default_build_number, pkg_name, vinca_conf):
+    """The build number a package of this configuration gets: the mutex has its own
+    (mutex_package.build_number, e.g. a new build at the same version), the others
+    the distribution's unless pkg_additional_info.yaml overrides it."""
+    mutex_config = parse_mutex_package_config(vinca_conf)
+    if mutex_config and pkg_name == mutex_config["name"]:
+        return mutex_config["build_number"]
+    return get_pkg_build_number(default_build_number, pkg_name, vinca_conf)
+
+
 def get_selected_packages(distro, vinca_conf):
     selected_packages = set()
     skipped_packages = set()
@@ -742,7 +752,7 @@ def main():
                 for _, pkg in all_pkgs.items():
                     is_built = False
                     if selected_bn is not None:
-                        pkg_build_number = get_pkg_build_number(
+                        pkg_build_number = expected_build_number(
                             selected_bn, pkg["name"], vinca_conf
                         )
                         if pkg["build_number"] == pkg_build_number:
diff --git a/vinca/mutex.py b/vinca/mutex.py
index b69a76f..8efd305 100644
--- a/vinca/mutex.py
+++ b/vinca/mutex.py
@@ -14,7 +14,8 @@
 
 from vinca.distro import Distro
 
-_REQUIRED_FIELDS = ("name", "version", "upper_bound", "run_constraints")
+# run_constraints is optional: a mutex only has to keep one distribution per environment
+_REQUIRED_FIELDS = ("name", "version", "upper_bound")
 
 
 def parse_mutex_package_config(vinca_conf: dict[str, Any]) -> dict[str, Any] | None:
@@ -102,7 +103,11 @@ def generate_mutex_package_recipe(
             "script": "",
         },
         "requirements": {
-            "run_constraints": mutex_config["run_constraints"],
+            **(
+                {"run_constraints": mutex_config["run_constraints"]}
+                if mutex_config.get("run_constraints")
+                else {}
+            ),
             "run_exports": {
                 "weak": [
                     f"${{{{ pin_subpackage('{name}', upper_bound='{mutex_config['upper_bound']}') }}}}"
diff --git a/vinca/template.py b/vinca/template.py
index 6873139..b4ab96c 100644
--- a/vinca/template.py
+++ b/vinca/template.py
@@ -131,8 +131,12 @@ def write_recipe(source, outputs, vinca_conf, distro, single_file=True):
                 o, distro, vinca_conf
             )
 
+            # an output's own build number (e.g. mutex_package.build_number) wins
+            # over the distribution's; pkg_additional_info.yaml overrides both
             meta["build"]["number"] = get_pkg_build_number(
-                vinca_conf.get("build_number", 0), package_name, vinca_conf
+                o.get("build", {}).get("number", vinca_conf.get("build_number", 0)),
+                package_name,
+                vinca_conf,
             )
             meta["build"]["post_process"] = post_process_items
 
diff --git a/vinca/test_mutex_build_number.py b/vinca/test_mutex_build_number.py
new file mode 100644
index 0000000..6232e98
--- /dev/null
+++ b/vinca/test_mutex_build_number.py
@@ -0,0 +1,67 @@
+"""mutex_package.build_number: a new build of the mutex at the same version."""
+
+from unittest.mock import Mock
+
+import yaml
+
+from vinca.main import expected_build_number
+from vinca.mutex import generate_mutex_package_recipe
+from vinca.template import write_recipe
+
+
+def _conf(**extra):
+    conf = {
+        "ros_distro": "lyrical",
+        "build_number": 27,
+        "mutex_package": {
+            "name": "ros2-distro-mutex",
+            "version": "0.21.0",
+            "upper_bound": "x.x",
+            "build_number": 28,
+        },
+        "_pkg_additional_info": {"rclcpp": {"build_number": 30}},
+        "_tests": {},
+    }
+    conf.update(extra)
+    return conf
+
+
+def test_expected_build_number_of_the_mutex_is_its_own():
+    assert expected_build_number(27, "ros2-distro-mutex", _conf()) == 28
+
+
+def test_expected_build_number_of_other_packages():
+    conf = _conf()
+    assert expected_build_number(27, "ros2-rclcpp", conf) == 30
+    assert expected_build_number(27, "ros2-std-msgs", conf) == 27
+
+
+def test_mutex_without_own_build_number_uses_the_distribution_one():
+    conf = _conf()
+    del conf["mutex_package"]["build_number"]
+    assert expected_build_number(27, "ros2-distro-mutex", conf) == 27
+
+
+def test_mutex_recipe_keeps_its_build_number(tmp_path, monkeypatch):
+    monkeypatch.chdir(tmp_path)
+    conf = _conf()
+    distro = Mock()
+    distro.name = "lyrical"
+    recipe = generate_mutex_package_recipe(conf, distro)
+    write_recipe({}, [recipe], conf, distro, single_file=False)
+    meta = yaml.safe_load(
+        (tmp_path / "recipes" / "ros2-distro-mutex" / "recipe.yaml").read_text()
+    )
+    assert meta["build"]["number"] == 28
+    assert meta["build"]["string"] == "lyrical_28"
+    # no (empty) run_constraints in the recipe
+    assert "run_constraints" not in meta["requirements"]
+
+
+def test_mutex_with_run_constraints_keeps_them():
+    conf = _conf()
+    conf["mutex_package"]["run_constraints"] = ["libfoo 1.*"]
+    distro = Mock()
+    distro.name = "lyrical"
+    recipe = generate_mutex_package_recipe(conf, distro)
+    assert recipe["requirements"]["run_constraints"] == ["libfoo 1.*"]