The classical Teichmüller-Wittich-Belinskii theorem implies the conformality of a planar continuous mapping at a point under rather general integral restrictions for the dilatation of this mapping near the distinguished point. This theorem is very rich in applications and has been generalized by many authors in various directions (weak conformality, differentiability, multidimensional analogs, etc.). Somewhat complete its generalizations to the mappings in Rn, n > 2, belong to Reshetnyak and Bishop-Gutlyanskii-Martio-Vuorinen. I will show in the talk that the assumptions of the Bishop-Gutlyanskii-Martio-Vuorinen theorem can be essentially weakened and give much stronger estimate for the limits of |f(x)|/|x| as x approaches 0. In the way, we essentially improve the underlying modular technique.