signal can rarely be justified in practice. We derive a simple analytical expression for the maximal possible asymptotic probability of correct detection, based on the sample covariance eigenvalues of the data, holding the asymptotic probability of false detection fixed. We find that the asymptotic probability of detection may be close to one even in cases where the strength of all signals is substantially below the phase transition threshold. This finding is, perhaps, surprising in light of the fact (P´ ech´ e, 2003) that in such cases, sometimes referred to as the sub-critical regime, the asymptotic behavior of any finite number of the largest sample covariance eigenvalues is not different from their behavior when the data are pure noise. We show that in these difficult cases, the detection power lies not in the different behavior of a few of the largest eigenvalues, but in the small deviations of the empirical distribution of all the eigenvalues from the Marchenko-Pastur limit (Marchenko and Pastur, 1967). Let us discuss our findings in more detail. We assume that data consist of n in- dependent observations of p -dimensional complex-valued Gaussian vectors X$_{t}$ with mean zero and covariance matrix σ $^{2}$( I$_{p}$ + V H ¯ V $^{′}$) , where I$_{p}$ is the p -dimensional identity matrix, σ is a real scalar, H is an r × r real diagonal matrix with elements h$_{j}$ ≥ 0 along the diagonal, and V is a ( p × r )-dimensional complex parameter normalized so that ¯ V $^{′}$V = I$_{r}$ . Such a spiked covariance model was proposed by Johnstone (2001) as a simple model of a situation, often observed in applications, where a few eigenvalues of the sample covariance matrix, corresponding to signals, are relatively large, whereas the rest of the eigenvalues are relatively small and tightly clustered. In our notation, the size of the spikes is regulated by the values of h$_{j}$, and the signal space is spanned by the columns of matrix V . Let λ$_{1}$ ≥ λ$_{2}$ ≥ ... ≥ λ$_{p}$ be the ordered eigenvalues of XX $^{′}$/n, where X = [ X$_{1}$, ..., X$_{n}$ ], and let λ = ( λ$_{1}$, ..., λ$_{m}$ ) , where m = min { n, p } . We are interested in the asymptotic power of tests for signal detection based on the information 3