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The performance of two-photon coherent-state (TCS) signals and integral-quantum signals in unimodal and bimodal free-space optical communications is compared with that of ordinary ,coherent signals under the constraint of fixed average error probability. For the unimodal channel of known phase the minimum attainable error probability for both on-off and antipodal TCS signals received in thermal noise is calculated by applying perturbation theory to the detection operator equation. For unimodal antipodal TCS signaling the threshold receiver is also considered. For channels of random phase the optimum photon-counting receiver is analyzed. In all cases the advantage of the nonclassical signal over an ordinary coherent signal vanishes as the transmittance of the channel goes to zero.