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The performance of dual-hop Decode-and-Forward relaying with relay selection (RS) is analyzed over Nakagami- fading channels. Assuming that the direct source-to-destination link is active, closed-form expressions for the moment generating and the cumulative distribution functions of a RS-based cooperation scheme that utilizes maximal-ratio diversity at the destination are derived. These expressions are used to obtain the outage probability (OP) and average symbol error probability (ASEP) of this pure RS scheme as well as of a rate-selective one that utilizes RS only when it provides higher achievable rate than that of the direct transmission. Numerically evaluated results, verified by computer simulations, show that, although, in terms of ASEP, relaying is always beneficial, in terms of OP, it should be disabled whenever the direct link is strong.