We propose and evaluate in this work a novel optimization strategy for intensity-based non-rigid image registration of contrast-enhanced images with a volume-preservation constraint. Since patient motion correction and volume preservation are to some extent mutually exclusive goals, one is usually faced with a trade-off between volume preservation of contrast-enhancing structures and artifact reduction. We address this problem by repeatedly applying registration passes with alternating incompressibility constraint weights. The novel optimization method alternates between under-constrained registration (allowing the elimination of motion artifacts in the subtraction images) and over-constrained registration (enforcing volume preservation of contrast-enhancing structures). We apply our method to pre- and post-contrast MR breast images from 17 patients. We evaluate our method and compare it to unconstrained and fixed constraint non-rigid registration by blinded visual assessment of maximum intensity projections of subtraction images. The alternating-constraints algorithm was judged to reduce artifacts better then the fixed-constraint algorithm in 11 out of 17 patients and equally well in the remaining 6. The results of this study show the capability of our method to achieve volume preservation and at the same time reduce artifacts very similar to what can be achieved by unconstrained non-rigid registration.