We investigate the frequency of complete sets for various complexity classes within EXP under several polynomial-time reductions in the sense of resource bounded measure. We show that these sets are scarce: The sets that are complete under 6 p n ?tt-reductions for NP, the levels of the polynomial-time hierarchy, and PSPACE have p 2-measure zero for any constant < 1. The 6 p n c ?T-complete sets...