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A simple three-mirror composite laser cavity is analyzed and optimum structures proposed in terms of the position of the central reflector and the value of its reflectivity in order to give single longitudinal mode operation. Two optimum structures are discussed, the first corresponding to relatively long cavities where a large period in the gain modulation is required in order to avoid a jump to the next mode with a high effective reflectivity, usually in a second mode group (as defined by a neighboring period of the gain modulation). The second corresponds to shorter lasers where jumps to neighboring modes should be avoided, since the spectral gain variation prevents jumps to other mode groups. The effects of mode discrimination due to external feedback have been analyzed and minimum values of reflectivity for the third mirror derived in order to preserve the internal mode selectivity.