To resist Binary Decision Diagrams (BDD) based attacks, a Boolean function should have a high BDD size. The hidden weighted bit function (HWBF), introduced by Bryant in 1991, seems to be the simplest function with exponential BDD size. In , Wang et al. investigated the cryptographic properties of the HWBF and found that it is a very good candidate for being used in real ciphers. In this paper, we modify the HWBF and construct two classes of functions with very good cryptographic properties (better than the HWBF). The new functions are balanced, with almost optimum algebraic degree and satisfy the strict avalanche criterion. Their nonlinearity is higher than that of the HWBF. We investigate their algebraic immunity, BDD size and their resistance against fast algebraic attacks, which seem to be better than those of the HWBF too. The new functions are simple, can be implemented efficiently have high BDD sizes and rather good cryptographic properties. Therefore they might be excellent candidates for constructions of real-life ciphers.