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This paper studies selective relaying schemes based on signal-to-noise-ratio (SNR) to minimize the end-to-end (e2e) bit error rate (BER) in cooperative digital relaying systems using BPSK modulation. In the SNR-based selective relaying, the relay either retransmits or remains silent depending on the SNRs of the source-relay, relay-destination, and source-destination links. Different models assuming the availability of different sets of instantaneous and average SNR information at the relay are studied. For each model, the optimal strategy to minimize the e2e BER is a different threshold rule on the source-relay SNR, if the link SNRs are uncorrelated in time and space. Approximations for the optimal threshold values that minimize the e2e BER and the resulting performance are derived analytically for BPSK modulation. Using the derived threshold the e2e BER can be reduced significantly compared to simple digital relaying. By studying the performance under different models, it is shown that knowledge of the instantaneous source-destination SNR at the relay can be exploited. The gain from this knowledge is higher when the average source-destination SNR is large. However, knowledge of the instantaneous relay-destination SNR at the relay does not change performance significantly.