The effects of applied pressure on deep defects, shallow ++ deep competition, and related doping problems in 11-VI semiconductors are reviewed. Photoluminescence studies to 100 kbar (at 7 K) on high purity ZnSe, and on several ZnSe samples doped with 10l6 to 10" cm-3 C1, Ga, N, P, and As reveal striking differences between the pressure-shifts of broad-band features involving acceptor and/or donor deep states, and excitonic lines due to shallow band-edge states. The binding energies of observed deep acceptor states tend to decrease with pressure, suggesting that compression acts to destabilize these states against competing shallow hole levels. A deep donor level assigned to an excited state of donor-vacancyz,, complexes emerges from the electron continuum in n-type Gaand C1-doped samples at -25 to 28 kbar. This previously unknown state should not affect doping in ZriSel-zTe, alloys since it arises from existing compensation centers.