We report an experimental investigation of 16 different mid-infrared diode laser samples with type-II "W" active regions. A number of design modifications were employed to study effects on the I-V characteristics, lasing threshold, and wallplug efficiency. Contrary to expectations, the threshold current density at low temperatures did not vary significantly with the number of active quantum-well periods, nor was there any clear correlation between lasing threshold and photoluminescence intensity. A shorter-wavelength device (3.2-3.6 mu m) produced > 500 mW of cw power at 80 K, and a second device displayed a wallplug efficiency > 10%. The maximum lasing temperature was 317 K for pulsed operation and 218 K for cw operation. At T = 100 K, cavity-length studies indicated an internal loss of 7 cm(-1) and nominal internal efficiency of 96%. Hakki-Paoli measurements of the gain spectrum implied an intrinsic linewidth enhancement factor of similar to 1.3, which slightly exceeds the theoretical prediction. Longer-wavelength devices (lambda approximate to 3.8-4.5 mu m) showed similarly low threshold current densities at T = 80 K but degraded more rapidly with increasing temperature.