  We extend and develop a method for perturbative calculations of anomalous
dimensions and mixing matrices of leading twist conformal primary operators in
conformal field theories. Such operators lie on the unitarity bound and hence
are conserved (irreducible) in the free theory. The technique relies on the
known pattern of breaking of the irreducibility conditions in the interacting
theory. We relate the divergence of the conformal operators via the field
equations to their descendants involving an extra field and accompanied by an
extra power of the coupling constant. The ratio of the two-point functions of
descendants and of their primaries determines the anomalous dimension, allowing
us to gain an order of perturbation theory. We demonstrate the efficiency of
the formalism on the lowest-order analysis of anomalous dimensions and mixing
matrices which is required for two-loop calculations of the former. We compare
these results to another method based on anomalous conformal Ward identities
and constraints from the conformal algebra. It also permits to gain a
perturbative order in computations of mixing matrices. We show the complete
equivalence of both approaches.
