While most previous studies of Hg-based mid-IR lasers have focused on either bulk Hg(1-x)Cd(x)Te alloys or thick (> 100 A) Hg(1-x)Cd(x)Te quantum wells with relatively large x, we show that much thinner (20-30 A) HgTe binary wells may be engineered to suppress both Auger recombination and intervalence free carrier absorption. On the basis of detailed numerical simulations, we predict 4.3 m cw emission at temperatures up to 220 K for optical pumping and 105 K for diode operation. In pulsed mode, we expect maximum lasing temperatures more than 100 K higher than any prior Hg-based mid-IR result.