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Constricted double-heterojunction (CDH) lasers are presented as the class of single-mode nonplanar-substrate devices for which the lasing cavity is on the least resistive electrical path between the contact and the substrate. Various types of CDH structures are considered under three general topics: liquid-phase epitaxy 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 the fundamental level; threshold-current temperature coefficients, as high as 375 C (pulsed) and 310 C (CW); constant external differential quantum efficiency to 100 C; and lasing operation to 170 C CW and 280 C pulsed. Semileakyguide CDH lasers have an asymmetric leaky cavity for lateral-mode confinement and provide single-mode operation to 15 to 20 mW/facet CW and to 50 mW/facet at 50% duty cycle. Modulation characteristics and preliminary reliability data are discussed.