In the presented research, the decision support in order to increase the efficiency of providing confidentiality of information with the use of methods of digital steganography is considered. These methods allow one to secretly transmit confidential information using various digital objects. When hiding information with the use of steganography, digital images are often used, among which compressed JPEG images are of the greatest popularity. The efficiency of information embedding into JPEG images substantially depends on properties of the source image used as a container. Therefore, in the considered field of information security, the relevant problem is to provide the decision support about the choice of digital cover objects that are the most suitable for the transmitting of the given amount of information. In the given paper, we provide an approach to the support of the selection of the best cover image out of a number of JPEG images, based on the application of the principles of optimality. The implementation of the given approach with the reference to the popular method of embedding (JSteg) is given. The results of experiments show that the considered approach allows us to select such an image from a set of cover images, for which the best visual quality of embedding is provided.