We report the first measurements demonstrating and quantifying the systematic reduction of the interface recombination velocity at the (Pb,Sn)Te/PbTe heterojunction interface with decreasing lattice-parameter mismatch. The relation between the degree of lattice-parameter mismatch and the interface recombination velocity is found to be sv = (2.9±0.3) ×107Δε/ε cm/sec. In conjunction with these measurements, we have also observed very low threshold current densities in laser devices fabricated with a small degree of lattice-parameter mimismatch. The lowest threshold current density observed was 15 A/cm2 in a Pb0.96Sn0.04Te/PbTe single-heterostructure laser with a 20-μm active-region width. This is the lowest current density ever reported in (Pb,Sn)Te-diode lasers.