The MXBean specification says that types other than the ones in a limited list are mapped into CompositeData with one item for every getter. It explicitly says that "getters must be public instance methods." But in fact it also includes public static getX() methods. For example, the class java.util.Locale would be allowed type in an MXBean according to the spec, but in fact it is disallowed because these two methods are included in the items for the CompositeData...
    public static Locale[] getAvailableLocales()
    public static Locale getDefault()
...and they imply an illegal self-referential type.