How do traditional redistricting principles—contiguity, communities of interest, political subdivisions, incumbent protection, Section 5 of the Voting Rights Act, preservation of district core, and compactness—affect racial minority representation in congressional districts? Using data from the 2001-02 redistricting process, we find that compactness is the only principle that significantly affects minority representation, both in terms of majority-minority districts and minority influence districts, but these effects are contingent on the size of the minority community and extent of racial segregation in a state. Two other principles, Section 5 pre-clearance and protecting political subdivisions, improve minority representation in a more limited way. Thus, race-neutral redistricting criteria like the compactness principle, can dramatically affect the racial composition of the resulting districts and, thereby, affect minority representation.