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We analyze the diversity-multiplexing tradeoff in a fading relay channel at finite signal-to-noise ratios (SNRs). In this framework, the rate adaptation policy is such that the target system data rate is a multiple of the capacity of an additive white Gaussian noise (AWGN) channel. The proportionality constant determines how aggressively the system scales the data rate and can be interpreted as a finite-SNR multiplexing gain. The diversity gain is given by the negative slope of the outage probability with respect to the SNR. Finite-SNR diversity performance is estimated using a constrained max-flow min-cut upper bound on the relay channel capacity. Moreover, the finite-SNR diversity-multiplexing tradeoff is characterized for three practical decode and forward half-duplex cooperative protocols with different amounts of broadcasting and simultaneous reception. For each configuration, system performance is computed as a function of SNR under a system-wide power constraint on the source and relay transmissions. Our analysis yields the following findings; (i) improved multiplexing performance can be achieved at any SNR by allowing the source to transmit constantly, (ii) both broadcasting and simultaneous reception are desirable in half-duplex relay cooperation for superior diversity-multiplexing performance, and (iii) the diversity-multiplexing tradeoff at finite-SNR is impacted by the power partitioning between the source and the relay terminals. Finally, we verify our analytical results by numerical simulations.