We present a reversible nonlinear discrete wavelet transform with predefined fixed wordsize based on lifting schemes. Restricting the dynamic range of the wavelet domain coefficients due to a fixed wordsize may result in overflow. We show how this overflow has to be handled in order to maintain reversibility of the transform. We also perform an analysis on how large a wordsize of the wavelet coefficients is needed to perform optimal lossless and lossy compressions of images. The scheme is advantageous to well-known integer-to-integer transforms since the wordsize of adders and multipliers can be predefined and does not increase steadily. This also results in significant gains in hardware implementations.