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We realized strongly index-coupled membrane buried-heterostructure (BH) distributed-feedback (DFB) lasers fabricated by electron-beam lithography, CH4/H2 reactive-ion etching, and regrowth by organometallic vapor-phase epitaxy, using surface corrugation DFB. First, we fabricated narrow stripe membrane BH-DFB lasers with surface corrugation for stable single-mode operation. Under optically pumped room-temperature continuous-wave (RT-CW) operation, a wide stopband width of 68 nm was observed in spite of the narrow stripe width of 0.6 mum. The corresponding index-coupling coefficient of 2950 cm-1 is over two times larger than that of a flat-surface (conventional) membrane BH-DFB laser with a stripe width of 2.0 mum. In addition, we fabricated a short-cavity membrane DFB laser with a surface corrugation structure. A threshold optical pump power of as low as 0.34 mW was realized for a 2.0-mum-wide and 80-mum-long device under RT-CW conditions.