The primary goal of image steganography techniques has been to maximize embedding rate while minimizing the detectability of the resulting stego images against steganalysis techniques. However, one particular advantage of steganography, as opposed to other information hiding techniques, is that the embedder has the freedom to choose a cover image that results in the least detectable stego image. This resource has largely remained unexploited in the proposed embedding techniques. In this paper, we study the problem of cover selection by investigating three scenarios in which the embedder has either no knowledge, partial knowledge, or full knowledge of the steganalysis technique. For example, we illustrate through experiments how simple statistical measures could help embedder minimize detectability, at times by 65%, in the partial knowledge case.