Jackson allows for finer grained control over which properties are serialized. The SET_PRIVATE_FIELDS_CONVENTION allows some flexibility by allowing private fields to be set directly. However, this could be extended to allow for greater flexibility.
An example of the ObjectMapper api allows flexibility for controlling: getter, setter and field properties:
mapper.setVisibility(IS_GETTER, NONE) .setVisibility(GETTER, NONE) .setVisibility(SETTER, NONE) .setVisibility(FIELD, ANY)