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The diversity performance of a multiple-input multiple-output (MIMO) wireless system is analyzed at finite signal-to-noise ratios (SNRs) when the data rate increases with SNR. The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. A lower bound on the outage probability of the MIMO system is used to characterize the diversity performance. It is seen that the achievable diversity gains at finite SNRs are significantly lower than asymptotic values given in the literature. This diversity characterization is useful in determining suitable rate adaptation strategies at realistic SNRs.