Integrated wavelets are a new method for discretizing the continuous wavelet transform (CWT). Independent of the choice of discrete scale and orientation parameters they yield tight families of convolution operators. Thus these families can easily be adapted to specific problems. After presenting the fundamental ideas, we focus primarily on the construction of directional integrated wavelets and their application to medical images. We state an exact algorithm for implementing this transform and present applications from the field of digital mammography. The first application covers the enhancement of microcalcifications in digital mammograms. Further, we exploit the directional information provided by integrated wavelets for better separation of microcalcifications from similar structures.