This paper presents three encoding strategies based on digital logic for steganography on Voice over IP (VoIP), which aim to enhance the embedding transparency. Differing from previous approaches, our strategies reduce the embedding distortion by improving the similarity between the cover and the covert message using digital logical transformations, instead of reducing the amount of the substitution bits. Therefore, by contrast, our strategies will improve the embedding transparency without sacrificing the embedding capacity. Of these three strategies, the first one adopts logical operations, the second one employs circular shifting operations, and the third one combines the operations of the first two. All of them are evaluated through comparing their prototype implementations with some existing methods in a prototypical covert communication system based on VoIP (called StegVoIP). The experimental results show that the proposed strategies can effectively enhance the embedding transparency while maintaining the maximum embedding capacity.