  Anomalous dimensions of Wilson operators with large Lorentz spin scale
logarithmically with the spin. Recent multi-loop QCD calculations of twist-two
anomalous dimensions revealed the existence of interesting structure of the
subleading corrections suppressed by powers of the Lorentz spin. We argue that
this structure is a manifestation of the `self-tuning' property of the
multi-loop anomalous dimensions - in a conformal gauge theory, the anomalous
dimension of Wilson operators is a function of their conformal spin which is
modified in higher loops by an amount proportional to the anomalous dimension.
Making use of the parity property of this function and incorporating the
beta-function contribution, we demonstrate the existence of (infinite number
of) relations between subleading corrections to the twist-two anomalous
dimensions in QCD and its supersymmetric extensions. They imply that the
subleading corrections to the anomalous dimensions suppressed by odd powers of
the conformal spin can be expressed in terms of the lower-loops corrections
suppressed by smaller even powers of the spin. We show that these relations
hold true in QCD to all loops in the large beta0 limit. In the N=4 SYM theory,
we employ the AdS/CFT correspondence to argue that the same relations survive
in the strong coupling regime for higher-twist scalar operators dual to a
folded string rotating on the AdS3xS1.
