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In this paper, we evaluate the performance of a selective-relaying (SR) protocol that is suitable for cooperative free-space optical (FSO) communications with any number of relays. The SR strategy is based on transmitting all information symbols either along the direct link between the source and the destination or along one of the indirect links via the relays. We derive closed-form expressions of upper-bounds on the average error probability that can be achieved over Rayleigh and lognormal fading channels. We also provide an asymptotic analysis for quantifying the diversity gain and reduction in fading variance that can be realized by the cooperative scheme. The performance analysis shows the superiority of the SR scheme over the strategy that corresponds to activating all available links.