Constricted double-heterojunction (CDH) diode lasers are presented as the class of nonplanar-substrate devices for which the laser cavity is one of the least resistive electrical path between the contact and the substrate. Various types of CDH structures are discussed while treating three general topics: liquid-phase epitaxy (LPE) over channeled substrates, lateral mode control, and current control in nonplanar-substrate devices. `Ridge-guide' CDH lasers have positive-index lateral mode confinement and provide: single-mode CW operation to 7 mW/facet at room temperature and to 3 mW/facet at 150°C, light-current characteristics with second-harmonic distortion as low as -57 dB below to fundamental level, threshold-current temperature coefficients T0 as high as 375° (pulsed) and 310° (CW), constant external differential quantum efficiency to 100°C, lasing operation to 170°C CW and 280°C pulsed. `Semileaky guide CDH lasers have an asymmetric leaky cavity for lateral mode confinement and provide; single-mode operation for 15-20 mW/facet CW, and to 50 mW/facet at 50 percent duty cycle. Modulation characteristics and preliminary reliability data are discussed.