  Level-restricted paths play an important role in crystal theory. They
correspond to certain highest weight vectors of modules of quantum affine
algebras. We show that the recently established bijection between
Littlewood--Richardson tableaux and rigged configurations is well-behaved with
respect to level-restriction and give an explicit characterization of
level-restricted rigged configurations. As a consequence a new general
fermionic formula for the level-restricted generalized Kostka polynomial is
obtained. Some coset branching functions of type $A$ are computed by taking
limits of these fermionic formulas.
