We consider uniform subclasses of the nonuniform complexity classes defined by Karp and Lipton via the notion of advice functions. These subclasses are obtained by restricting the complexity of computing correct advice. We also investigate the effect of allowing advice functions of limited complexity to depend on the input rather than on the input's length. Among other results, using the notions described above, we give new characterizations of

- SPARSE(NP),
- NP with a restricted access to an NP oracle, and
- the odd levels of the Boolean hierarchy.