We present a systematic study of higher-twist distribution amplitudes (DAs) of the B-meson which give rise to power-suppressed 1/m(B) contributions to B-decays in final states with energetic light particles in the framework of QCD factorization. As the main result, we find that the renormalization group equations for the three-particle distributions are completely integrable in the large N-c limit and can be solved exactly. General properties of the solutions are studied. We propose simple models for higher-twist DAs which satisfy all existing constraints and can be used in phenomenological studies.