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We consider the use of entropy maximization methods as a tool to generate fading models for multiple-input multiple-output (MIMO) spatially correlated flat-fading channels. We focus in particular on various assumptions about the degree of knowledge on the full covariance matrix of the channel (namely in the power constraint, rank constraint, and average constraint case). We show that this method can provide closed-form probability density functions in all cases. In a second part, we analyze the statistical properties of the singular values of the resulting fading channel. In general, they are more spread out that in the classical Gaussian i.i.d. case, which incurs less optimistic ergodic capacity figures.