: The paper is concerned with hiding information into a digital image, specifically, an English text is used to be hidden into a digital grey-scale image. The purpose of this research is to embed a maximum text data size into the most suitable image selected among several images based on the binary entropy function measurements of both the text and image. The embedding process is constrained by minimising the bit error rate. Our results show that the binary entropy function can be considered as a powerful tool to select a proper image for a predetermined text under the BER constrain.