  Mazur's principle gives a criterion under which an irreducible mod l Galois
representation arising from a classical modular form of level Np (with p prime
to N) also arises from a classical modular form of level N. We consider the
analogous question for Galois representations arising from certain unitary
Shimura varieties. In particular, we prove an analoge of Mazur's principle for
U(2,1) Shimura varities. We also give a conjectural criterion for a Galois
representation arising in the cohomology of a unitary Shimura variety whose
level subgroup is parahoric at p to also arise in the cohomology of a Shimura
variety with "less level structure at p".

Number Theory