Based on a careful analysis of functional models for contractive multi-analytic operators we have established a one-to-one correspondence between unitary equivalence classes of minimal contractive liftings of a row contraction and injective symbols of contractive multi-analytic operators. This allows an effective construction and classification of all such liftings with given defects. G. Popescu’s theory of characteristic functions of completely non-coisometric row contractions is obtained as a special case satisfying a Szeg ̈o condition. In another special case of single contractions and defects equal to 1 all non-zero Schur functions on the unit disk appear in the classification. It is also shown that the process of constructing liftings iteratively reflects itself in a factorization of the corresponding symbols.