diff --git a/tests/test_types_basic.py b/tests/test_types_basic.py
index 13b6e614..7a5293f9 100644
--- a/tests/test_types_basic.py
+++ b/tests/test_types_basic.py
@@ -38,6 +38,19 @@ class TE(t.enum_flag_uint16):
     assert TE(0x8012).serialize() == data
 
 
+def test_abstract_ints():
+    assert issubclass(t.uint8_t, t.uint_t)
+    assert not issubclass(t.uint8_t, t.int_t)
+    assert t.int_t._signed is True
+    assert t.uint_t._signed is False
+
+    with pytest.raises(TypeError):
+        t.int_t(0)
+
+    with pytest.raises(TypeError):
+        t.FixedIntType(0)
+
+
 def test_int_too_short():
     with pytest.raises(ValueError):
         t.uint8_t.deserialize(b"")
@@ -159,3 +172,11 @@ class TestList(t.FixedList, length=3, item_type=t.uint16_t):
     assert r[0] == 0x1234
     assert r[1] == 0xAA55
     assert r[2] == 0xAB89
+
+
+def test_enum_instance_types():
+    class TestEnum(t.enum_uint8):
+        Member = 0x00
+
+    assert TestEnum._member_type_ is t.uint8_t
+    assert type(TestEnum.Member.value) is t.uint8_t
diff --git a/tests/test_types_named.py b/tests/test_types_named.py
index 19f845f8..ae6b56a2 100644
--- a/tests/test_types_named.py
+++ b/tests/test_types_named.py
@@ -95,13 +95,21 @@ def test_addr_mode_address():
 
 
 def test_missing_status_enum():
-    assert 0x33 not in list(t.Status)
-    assert isinstance(t.Status(0x33), t.Status)
-    assert t.Status(0x33).value == 0x33
+    class TestEnum(t.MissingEnumMixin, t.enum_uint8):
+        Member = 0x00
 
-    # Status values that don't fit can't be created
+    assert 0xFF not in list(TestEnum)
+    assert isinstance(TestEnum(0xFF), TestEnum)
+    assert TestEnum(0xFF).value == 0xFF
+    assert type(TestEnum(0xFF).value) is t.uint8_t
+
+    # Missing members that don't fit can't be created
+    with pytest.raises(ValueError):
+        TestEnum(0xFF + 1)
+
+    # Missing members that aren't integers can't be created
     with pytest.raises(ValueError):
-        t.Status(0xFF + 1)
+        TestEnum("0xFF")
 
 
 def test_zdo_nullable_node_descriptor():
diff --git a/zigpy_znp/types/basic.py b/zigpy_znp/types/basic.py
index f9cf476e..9a511b1d 100644
--- a/zigpy_znp/types/basic.py
+++ b/zigpy_znp/types/basic.py
@@ -24,18 +24,32 @@ def serialize_list(objects) -> Bytes:
     return Bytes(b"".join([o.serialize() for o in objects]))
 
 
-class int_t(int):
-    _signed = True
+class FixedIntType(int):
+    _signed = None
     _size = None
 
+    def _concrete_new(cls, value=0):
+        instance = super().__new__(cls, value)
+        instance.serialize()
+
+        return instance
+
     def __new__(cls, value):
-        instance = int.__new__(cls, value)
+        raise TypeError(f"Instances of abstract type {cls} cannot be created")
 
-        if instance._signed is not None and instance._size is not None:
-            # It's a concrete int_t type, check to make sure it's valid
-            instance.serialize()
+    def __init_subclass__(cls, signed=None, size=None, **kwargs) -> None:
+        if signed is not None:
+            cls._signed = signed
 
-        return instance
+        if size is not None:
+            cls._size = size
+
+        # XXX: The enum module uses the first class with `__new__` in its `__dict__`
+        #      as the member type. We have to give each subclass its own `__new__`.
+        if signed is not None or size is not None:
+            cls.__new__ = cls._concrete_new
+
+        super().__init_subclass__(**kwargs)
 
     def serialize(self) -> bytes:
         try:
@@ -54,72 +68,76 @@ def deserialize(cls, data: bytes) -> typing.Tuple["int_t", bytes]:
         return r, data
 
 
-class int8s(int_t):
-    _size = 1
+class uint_t(FixedIntType, signed=False):
+    pass
 
 
-class int16s(int_t):
-    _size = 2
+class int_t(FixedIntType, signed=True):
+    pass
+
+
+class int8s(int_t, size=1):
+    pass
 
 
-class int24s(int_t):
-    _size = 3
+class int16s(int_t, size=2):
+    pass
 
 
-class int32s(int_t):
-    _size = 4
+class int24s(int_t, size=3):
+    pass
 
 
-class int40s(int_t):
-    _size = 5
+class int32s(int_t, size=4):
+    pass
 
 
-class int48s(int_t):
-    _size = 6
+class int40s(int_t, size=5):
+    pass
 
 
-class int56s(int_t):
-    _size = 7
+class int48s(int_t, size=6):
+    pass
 
 
-class int64s(int_t):
-    _size = 8
+class int56s(int_t, size=7):
+    pass
 
 
-class uint_t(int_t):
-    _signed = False
+class int64s(int_t, size=8):
+    pass
 
 
-class uint8_t(uint_t):
-    _size = 1
+class uint8_t(uint_t, size=1):
+    pass
 
 
-class uint16_t(uint_t):
-    _size = 2
+class uint16_t(uint_t, size=2):
+    pass
 
 
-class uint24_t(uint_t):
-    _size = 3
+class uint24_t(uint_t, size=3):
+    pass
 
 
-class uint32_t(uint_t):
-    _size = 4
+class uint32_t(uint_t, size=4):
+    pass
 
 
-class uint40_t(uint_t):
-    _size = 5
+class uint40_t(uint_t, size=5):
+    pass
 
 
-class uint48_t(uint_t):
-    _size = 6
+class uint48_t(uint_t, size=6):
+    pass
 
 
-class uint56_t(uint_t):
-    _size = 7
+class uint56_t(uint_t, size=7):
+    pass
 
 
-class uint64_t(uint_t):
-    _size = 8
+class uint64_t(uint_t, size=8):
+    pass
 
 
 class ShortBytes(Bytes):
diff --git a/zigpy_znp/types/named.py b/zigpy_znp/types/named.py
index d6321fd1..8f7451d8 100644
--- a/zigpy_znp/types/named.py
+++ b/zigpy_znp/types/named.py
@@ -149,14 +149,12 @@ class Schema:
 class MissingEnumMixin:
     @classmethod
     def _missing_(cls, value):
-        if not isinstance(value, int) or value < 0 or value > 0xFF:
-            # `return None` works with Python 3.7.7, breaks with 3.7.1
+        if not isinstance(value, int):
             raise ValueError(f"{value} is not a valid {cls.__name__}")
 
-        # XXX: infer type from enum
-        new_member = basic.uint8_t.__new__(cls, value)
+        new_member = cls._member_type_.__new__(cls, value)
         new_member._name_ = f"unknown_0x{value:02X}"
-        new_member._value_ = value
+        new_member._value_ = cls._member_type_(value)
 
         if sys.version_info >= (3, 8):
             # Show the warning in the calling code, not in this function