In recent times, the use of Internet for data exchange has increased to a great extent. Steganography, cryptography and watermarking are the methods to transfer the data with high security. In this paper, a steganography method with constant bit embedding and adaptive bit embedding in Haar Integer Wavelet Transform domain has been proposed. The adaptive bit embedding provides more security than the constant bit embedding. Here, a mathematical model for Knight's Tour is developed, which adapts random traversing inside the wavelet coefficients to increase the security further. In this proposed work, multiple security is ensured by formulating Knight's Tour algorithm for random traversing and selecting the order of sub-bands to provide high capacity, security and robustness. Copyright © 2015 John Wiley & Sons, Ltd.