diff --git a/src/cattrs/enums.py b/src/cattrs/enums.py
index b1ab5040..94d73e29 100644
--- a/src/cattrs/enums.py
+++ b/src/cattrs/enums.py
@@ -1,20 +1,37 @@
-from collections.abc import Callable
+from collections.abc import Callable, Mapping
 from enum import Enum
 from typing import TYPE_CHECKING, Any
 
+from ._compat import has
+
 if TYPE_CHECKING:
     from .converters import BaseConverter
 
 
+def _needs_recursive_unstructure(value: Any) -> bool:
+    if isinstance(value, Enum) or has(value.__class__):
+        return True
+    if isinstance(value, tuple | list | set | frozenset):
+        return any(_needs_recursive_unstructure(v) for v in value)
+    if isinstance(value, Mapping):
+        return any(
+            _needs_recursive_unstructure(k) or _needs_recursive_unstructure(v)
+            for k, v in value.items()
+        )
+    return False
+
+
 def enum_unstructure_factory(
     type: type[Enum], converter: "BaseConverter"
 ) -> Callable[[Enum], Any]:
     """A factory for generating enum unstructure hooks.
 
     If the enum is a typed enum (has `_value_`), we use the underlying value's hook.
-    Otherwise, we use the value directly.
+    Otherwise, we only use the converter when the values are known to need it.
     """
-    if "_value_" in type.__annotations__:
+    if "_value_" in type.__annotations__ or any(
+        _needs_recursive_unstructure(member.value) for member in type
+    ):
         return lambda e: converter.unstructure(e.value)
 
     return lambda e: e.value
diff --git a/tests/test_enums.py b/tests/test_enums.py
index bdf591f1..5a58f2ae 100644
--- a/tests/test_enums.py
+++ b/tests/test_enums.py
@@ -2,6 +2,7 @@
 
 from enum import Enum
 
+from attrs import define
 from hypothesis import given
 from hypothesis.strategies import data, sampled_from
 from pytest import raises
@@ -68,3 +69,57 @@ def test_structure_complex_enum() -> None:
     assert converter.structure(0, SimpleEnum) == SimpleEnum.A
     assert converter.structure("E", SimpleEnumWithTypeHint) == SimpleEnumWithTypeHint.E
     assert converter.structure((0, "D"), ComplexEnum) == ComplexEnum.AD
+
+
+class EnumValuedEnum(Enum):
+    """Enum whose members have other Enum instances as values (no type annotation)."""
+
+    X = SimpleEnum.A
+    Y = SimpleEnum.B
+
+
+class TupleValuedEnum(Enum):
+    """Enum whose members have tuples with Enum instances (no type annotation)."""
+
+    X = (SimpleEnum.A, 1)
+
+
+@define
+class AnAttrsClass:
+    a: int
+
+
+class AttrsValuedEnum(Enum):
+    """Enum whose members have attrs instances as values (no type annotation)."""
+
+    X = AnAttrsClass(1)
+
+
+def test_unstructure_simple_enum_uses_value_directly() -> None:
+    """Simple enum values do not recurse through the converter."""
+    converter = BaseConverter()
+    converter.register_unstructure_hook(int, lambda _: "overridden")
+
+    assert converter.unstructure(SimpleEnum.A) == 0
+
+
+def test_unstructure_enum_with_enum_values() -> None:
+    """Enum members whose values are themselves Enums are unstructured recursively.
+
+    Regression test for https://github.com/python-attrs/cattrs/issues/679.
+    """
+    converter = BaseConverter()
+    assert converter.unstructure(EnumValuedEnum.X) == 0
+    assert converter.unstructure(EnumValuedEnum.Y) == 1
+
+
+def test_unstructure_enum_with_tuple_values() -> None:
+    """Enum member tuples containing Enums are unstructured recursively."""
+    converter = BaseConverter()
+    assert converter.unstructure(TupleValuedEnum.X) == (0, 1)
+
+
+def test_unstructure_enum_with_attrs_values() -> None:
+    """Enum members whose values are attrs classes are unstructured recursively."""
+    converter = BaseConverter()
+    assert converter.unstructure(AttrsValuedEnum.X) == {"a": 1}