diff --git a/dbus/dbus-internals.c b/dbus/dbus-internals.c
index 2c4336773b3d8067206ee072d4f757a4484c2049..3e578eb50530039c4a859ae98b8bfa93dfa3efe5 100644
--- a/dbus/dbus-internals.c
+++ b/dbus/dbus-internals.c
@@ -177,6 +177,35 @@
  * Unlocks a global lock
  */
 
+/* The build system should have checked for DBUS_SIZEOF_VOID_P */
+_DBUS_STATIC_ASSERT (sizeof (void *) == DBUS_SIZEOF_VOID_P);
+
+/* dbus currently assumes that function pointers are essentially
+ * interchangeable with data pointers. There's nothing special about
+ * DBusShutdownFunction, it's just an arbitrary function pointer type.
+ * If this assertion fails on your platform, some porting will be required. */
+_DBUS_STATIC_ASSERT (sizeof (void *) == sizeof (DBusShutdownFunction));
+_DBUS_STATIC_ASSERT (_DBUS_ALIGNOF (void *) == _DBUS_ALIGNOF (DBusShutdownFunction));
+
+/* This is meant to be true by definition. */
+_DBUS_STATIC_ASSERT (sizeof (void *) == sizeof (intptr_t));
+_DBUS_STATIC_ASSERT (sizeof (void *) == sizeof (uintptr_t));
+
+/*
+ * Some frequent assumptions that we should *avoid* making include these,
+ * all of which are false on CHERI (which has 128-bit tagged pointers,
+ * but a 64-bit address space and therefore 64-bit sizes):
+ *
+ * sizeof (void *) <= sizeof (size_t)
+ * sizeof (void *) <= 8
+ * _DBUS_ALIGNOF (void *) <= 8
+ *
+ * We should also avoid making these assumptions, although we don't currently
+ * know a concrete example of platforms where they're false:
+ *
+ * sizeof (ptrdiff_t) == sizeof (size_t)
+ */
+
 /**
  * Fixed "out of memory" error message, just to avoid
  * making up a different string every time and wasting
diff --git a/dbus/dbus-marshal-basic.c b/dbus/dbus-marshal-basic.c
index 938e29230d2c963ea6a061b3d322e6d8f94ba2b4..1f5d54a4eedc5505f9ce544d2efc43663be9ec25 100644
--- a/dbus/dbus-marshal-basic.c
+++ b/dbus/dbus-marshal-basic.c
@@ -30,19 +30,10 @@
 
 #include <string.h>
 
-#if defined(__GNUC__) && (__GNUC__ >= 4)
-# define _DBUS_ASSERT_ALIGNMENT(type, op, val) \
-  _DBUS_STATIC_ASSERT (__extension__ __alignof__ (type) op val)
-# define _DBUS_ASSERT_CMP_ALIGNMENT(left, op, right) \
-  _DBUS_STATIC_ASSERT (__extension__ __alignof__ (left) op __extension__ __alignof__ (right))
-#else
-  /* not gcc, so probably no alignof operator: just use a no-op statement
-   * that's valid in the same contexts */
-# define _DBUS_ASSERT_ALIGNMENT(type, op, val) \
-  _DBUS_STATIC_ASSERT (TRUE)
-# define _DBUS_ASSERT_CMP_ALIGNMENT(left, op, right) \
-  _DBUS_STATIC_ASSERT (TRUE)
-#endif
+#define _DBUS_ASSERT_ALIGNMENT(type, op, val) \
+  _DBUS_STATIC_ASSERT (_DBUS_ALIGNOF (type) op val)
+#define _DBUS_ASSERT_CMP_ALIGNMENT(left, op, right) \
+  _DBUS_STATIC_ASSERT (_DBUS_ALIGNOF (left) op _DBUS_ALIGNOF (right))
 
 /* True by definition, but just for completeness... */
 _DBUS_STATIC_ASSERT (sizeof (char) == 1);