diff --git a/include/nanobind/nb_class.h b/include/nanobind/nb_class.h
index 6ddff294..6825c987 100644
--- a/include/nanobind/nb_class.h
+++ b/include/nanobind/nb_class.h
@@ -58,16 +58,10 @@ enum class type_flags : uint32_t {
     /// The class implements __class_getitem__ similar to typing.Generic
     is_generic               = (1 << 15),
 
-    /// Is this an arithmetic enumeration?
-    is_arithmetic            = (1 << 16),
-
-    /// Is the number type underlying the enumeration signed?
-    is_signed                = (1 << 17),
-
     /// Does the type implement a custom __new__ operator?
-    has_new                  = (1 << 18)
+    has_new                  = (1 << 16)
 
-    // No more bits bits available without needing a larger reorganization
+    // Two more bits bits available without needing a larger reorganization
 };
 
 /// Flags about a type that are only relevant when it is being created.
@@ -192,6 +186,14 @@ NB_INLINE void type_extra_apply(type_init_data &t, supplement<T>) {
     t.supplement = sizeof(T);
 }
 
+enum class enum_flags : uint32_t {
+    /// Is this an arithmetic enumeration?
+    is_arithmetic            = (1 << 1),
+
+    /// Is the number type underlying the enumeration signed?
+    is_signed                = (1 << 2)
+};
+
 struct enum_init_data {
     const std::type_info *type;
     PyObject *scope;
@@ -201,7 +203,7 @@ struct enum_init_data {
 };
 
 NB_INLINE void enum_extra_apply(enum_init_data &e, is_arithmetic) {
-    e.flags |= (uint32_t) type_flags::is_arithmetic;
+    e.flags |= (uint32_t) enum_flags::is_arithmetic;
 }
 
 NB_INLINE void enum_extra_apply(enum_init_data &e, const char *doc) {
@@ -719,7 +721,7 @@ template <typename T> class enum_ : public object {
         ed.scope = scope.ptr();
         ed.name = name;
         ed.flags = std::is_signed_v<Underlying>
-                       ? (uint32_t) detail::type_flags::is_signed
+                       ? (uint32_t) detail::enum_flags::is_signed
                        : 0;
         (detail::enum_extra_apply(ed, extra), ...);
         m_ptr = detail::enum_create(&ed);
diff --git a/src/nb_enum.cpp b/src/nb_enum.cpp
index d81d415d..2969be9e 100644
--- a/src/nb_enum.cpp
+++ b/src/nb_enum.cpp
@@ -27,7 +27,7 @@ PyObject *enum_create(enum_init_data *ed) noexcept {
 
     handle scope(ed->scope);
 
-    bool is_arithmetic = ed->flags & (uint32_t) type_flags::is_arithmetic;
+    bool is_arithmetic = ed->flags & (uint32_t) enum_flags::is_arithmetic;
 
     str name(ed->name), qualname = name;
     object modname;
@@ -99,7 +99,7 @@ void enum_append(PyObject *tp_, const char *name_, int64_t value_,
     type_data *t = enum_get_type_data(tp);
 
     object val;
-    if (t->flags & (uint32_t) type_flags::is_signed)
+    if (t->flags & (uint32_t) enum_flags::is_signed)
         val = steal(PyLong_FromLongLong((long long) value_));
     else
         val = steal(PyLong_FromUnsignedLongLong((unsigned long long) value_));
@@ -161,7 +161,7 @@ bool enum_from_python(const std::type_info *tp, PyObject *o, int64_t *out, uint8
     if (flags & (uint8_t) cast_flags::convert) {
         enum_map *fwd = (enum_map *) t->enum_tbl.fwd;
 
-        if (t->flags & (uint32_t) type_flags::is_signed) {
+        if (t->flags & (uint32_t) enum_flags::is_signed) {
             long long value = PyLong_AsLongLong(o);
             if (value == -1 && PyErr_Occurred()) {
                 PyErr_Clear();
@@ -204,7 +204,7 @@ PyObject *enum_from_cpp(const std::type_info *tp, int64_t key) noexcept {
         return value;
     }
 
-    if (t->flags & (uint32_t) type_flags::is_signed)
+    if (t->flags & (uint32_t) enum_flags::is_signed)
         PyErr_Format(PyExc_ValueError, "%lli is not a valid %s.",
                      (long long) key, t->name);
     else