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Space-time code (STC) designs commonly rely on the assumptions of independent and identically distributed (i.i.d.) Rayleigh channels (being either slow or fast fading) and high signal-to-noise ratio (SNR). However, it has been shown that poor scattering conditions can have detrimental effects on the performance of STCs and that the behavior of codes at high SNR is radically different from the finite SNR behavior. This calls for new design criteria that correctly predict the behavior of codes in correlated channels at finite SNR. In this paper, we investigate how spatially and temporally correlated Ricean fading affects the performance of STCs at finite SNR. We derive a code design criterion leading to robust STCs in a wide variety of propagation conditions and do not require any channel knowledge at the transmitter. Codes satisfying this criterion are shown to perform sensibly better in correlated channels than codes designed only for i.i.d. slow or fast Rayleigh-fading channels. Examples of space-time trellis codes and algebraic codes are proposed in order to illustrate the developed criterion.