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We present a theoretical study of the effect of radiation losses on the mode selectivity of DFB lasers with second-order gratings. For a second-order grating, interference of the radiation due to first-order diffraction of oppositely propagating guided waves cancels the radiation loss at one of the edges of the spectrum gap. This provides threshold gain discrimination of order 10 cm-1against one of the two dominant modes occurring near the edges of the gap. This should allow fabrication of DFB lasers with properties that are nearly independent of the positions of the facets relative to the grating corrugations, which are uncontrolled. By applying antireflection coatings to the two ends, differential quantum efficiencies close to those of conventional Fabry-Perot lasers should be achievable.