The steganography point is in that, the fact of confidential data existence in some container was a secret for the third parties. Methods of the digital steganography allow to hide an information in different digital objects: images, audio-and video files. In particular, information hiding in digital images can be used successfully for its subsequent imperceptible storage and transmission, for example, exchange of images in the Internet is a commonplace and will not draw attention. However changes made to data items of digital images in case of steganographic embedding can cause essential distortions of the received stego-image, and attachments can be found. Therefore the approach allowing to reduce quantity of the changes made to data items of digital images when embedding is offered. This approach is directed on increase in efficiency of steganographic embedding of information into a phase spectrum of the discrete Fourier transformation (DFT) of digital images. Feature of the offered approach is minimization of quantity of changes made to frequency coefficients. The approach is applied for improvement of earlier developed (by authors of this paper) algorithm of faultless information embedding into a phase spectrum of the DFT of digital images. Computing experiments' results confirm that the offered approach allows to increase embedding quality and capacity of the image container at the same time.