Type II "W" diodes designed for emission at the spectral line of methane (3.31 mu m) when operated near 80 K were grown on a compact 21T RIBER molecular beam epitaxy system. Photoluminescence and cross-sectional scanning tunneling microscopy were used as tools to improve the growth quality of these structures. The diodes exhibited very low lasing thresholds at T=80 K (24-40 A /cm(2)), although further development will be required to enhance the characteristic temperature (T(0)similar to 40 K) and the maximum operating temperature (similar to 190 K). The lasers had favorable internal losses at all T up to 190 K (similar to 7 cm(-1)), and favorable internal efficiencies at low T (up to 85%). The I-V characteristics of nonlasing test structures were improved substantially by adding n-side "transition" regions that smoothed out abrupt steps in the conduction-band offset.