Wavelets are often characterized through their number of vanishing moments. The more vanishing moments a wavelet has the better are the compaction properties for low-order polynomial signals. However, when bounding wavelets on intervals in order to define wavelet transforms over regions of arbitrary support, some of the moment properties get lost. This is typically accompanied with a loss of compaction gain and other unwanted effects. In this paper, we present methods for recovering the moment properties in the boundary regions. The approach recovers the moments step by step, requires a low number of computations and is well suited for the implementation with finite-precision arithmetic. 1 INTRODUCTION The discrete wavelet transform (DWT) is known to be one of the most efficient tools for image compression . The principle of this transform is to hierarchically decompose a signal into a multiresolution pyramid, where the signal is split into a coarse approximation and some detail i..