We prove that if for some &epsilon > 0, NP contains a set that is DTIME(2n&epsilon)-bi-immune, then NP contains a set that is 2-Turing complete for NP (hence 3-truth-table complete) but not 1-truth-table complete for NP. Thus this hypothesis implies a strong separation of completeness notions for NP. Lutz and Mayordomo (1996) and Ambos-Spies and Bentzien (2000) previously obtained the same consequence using strong hypotheses involving resource-bounded measure and/or category theory. Our hypothesis is weaker and involves no assumptions about stochastic properties of NP.