diff --git a/lib/elixir/lib/module/types/descr.ex b/lib/elixir/lib/module/types/descr.ex
index 90e49b3772d..0400ad8c5a0 100644
--- a/lib/elixir/lib/module/types/descr.ex
+++ b/lib/elixir/lib/module/types/descr.ex
@@ -1603,7 +1603,7 @@ defmodule Module.Types.Descr do
 
   defp fun_normalize(%{fun: {:union, bdds}}, arity) do
     case :maps.take(arity, bdds) do
-      {bdd, _rest} ->
+      {bdd, rest} ->
         {domain, arrows} =
           Enum.reduce(fun_bdd_to_pos_dnf(arity, bdd), {term(), []}, fn pos_funs,
                                                                        {domain, arrows} ->
@@ -1611,7 +1611,13 @@ defmodule Module.Types.Descr do
           end)
 
         if arrows == [] do
-          {:badarity, :maps.keys(bdds)}
+          # The function is empty at the requested arity. Report the *other*
+          # arities (never the called one, which would be self-contradictory),
+          # or :badfun when there are none, i.e. the function is empty.
+          case :maps.keys(rest) do
+            [] -> :badfun
+            other -> {:badarity, other}
+          end
         else
           {:ok, domain, arrows}
         end
diff --git a/lib/elixir/test/elixir/module/types/descr_test.exs b/lib/elixir/test/elixir/module/types/descr_test.exs
index 78c8f252eb3..a0f6f0ec1e3 100644
--- a/lib/elixir/test/elixir/module/types/descr_test.exs
+++ b/lib/elixir/test/elixir/module/types/descr_test.exs
@@ -1378,6 +1378,28 @@ defmodule Module.Types.DescrTest do
       assert fun_apply(fun_mixed, [integer()]) == {:badarity, [1, 2]}
       assert fun_apply(fun_mixed, [integer(), atom()]) == {:badarity, [2, 1]}
 
+      # A function that is empty at the called arity is :badfun, not a
+      # self-contradictory {:badarity, [called_arity]}.
+      empty_fun =
+        opt_difference(fun([opt_union(integer(), float())], atom()), fun([integer()], atom()))
+
+      assert empty?(empty_fun)
+      assert fun_apply(empty_fun, [integer()]) == :badfun
+
+      # When the function is empty at the called arity but usable at another, the
+      # badarity must list only the *other* arity, never the (empty) called one.
+      # `empty_fun` keeps a structured empty arity-1 entry, which union preserves,
+      # so `usable_at_2` is equal? to a plain 2-arity function yet carries it.
+      usable_at_2 = opt_union(empty_fun, fun([integer(), atom()], boolean()))
+
+      refute empty?(usable_at_2)
+      assert equal?(usable_at_2, fun([integer(), atom()], boolean()))
+
+      # Congruent with the normalized form, and excludes the empty arity 1.
+      assert fun_apply(usable_at_2, [integer()]) == {:badarity, [2]}
+      assert fun_apply(fun([integer(), atom()], boolean()), [integer()]) == {:badarity, [2]}
+      assert fun_apply(usable_at_2, [integer(), atom()]) == {:ok, boolean()}
+
       # Function intersection tests (no overlap)
       fun0 = opt_intersection(fun([integer()], atom()), fun([float()], binary()))
       assert fun_apply(fun0, [integer()]) == {:ok, atom()}