diff --git a/src/lob_hlpr/cli.py b/src/lob_hlpr/cli.py
index ec00461..78f406c 100644
--- a/src/lob_hlpr/cli.py
+++ b/src/lob_hlpr/cli.py
@@ -8,6 +8,10 @@
 
 _LOGGER = logging.getLogger(__name__)
 
+# Actions whose value DeprecatedAliasAction can store the same way. Others such
+# as append or count build on the previous value, which the alias would lose.
+_ALIASABLE_ACTIONS = (None, "store", "store_true", "store_false", "store_const")
+
 
 class DeprecatedAliasAction(argparse.Action):
     """Store a value like the option it replaces, but say it is out of date.
@@ -55,6 +59,11 @@ def add_renamed_argument(
     Returns:
         The action for the current option.
 
+    Raises:
+        ValueError: For ``required=True``, which argparse checks per spelling
+            so the old one could never satisfy it, and for actions other than
+            the store ones, such as ``append`` or ``count``.
+
     Example:
         >>> parser = argparse.ArgumentParser()
         >>> _ = add_renamed_argument(
@@ -63,6 +72,10 @@ def add_renamed_argument(
         >>> parser.parse_args(["--loglevel", "DEBUG"]).log_level
         'DEBUG'
     """
+    if kwargs.get("required"):
+        raise ValueError("A renamed option cannot be required")
+    if kwargs.get("action") not in _ALIASABLE_ACTIONS:
+        raise ValueError(f"A renamed option cannot use action={kwargs['action']!r}")
     action = parser.add_argument(*flags, **kwargs)
     # argparse's own default for these is not None, so only forward the ones the
     # current option actually set.
diff --git a/tests/test_cli.py b/tests/test_cli.py
index 56668cb..f8f1b36 100644
--- a/tests/test_cli.py
+++ b/tests/test_cli.py
@@ -88,6 +88,18 @@ def test_a_flag_without_a_value_can_be_renamed():
         assert parser.parse_args(["--nogui"]).no_gui is True
 
 
+@pytest.mark.parametrize(
+    "kwargs",
+    [{"required": True}, {"action": "append"}, {"action": "count"}],
+    ids=["required", "append", "count"],
+)
+def test_unsupported_options_are_rejected(kwargs):
+    """Options the alias cannot mirror fail when added, not when parsed."""
+    parser = argparse.ArgumentParser("test")
+    with pytest.raises(ValueError):
+        add_renamed_argument(parser, "--new", deprecated="--old", **kwargs)
+
+
 def test_several_old_spellings_can_be_kept_alive():
     """An option renamed twice should not need two helpers."""
     parser = argparse.ArgumentParser("test")