  We discuss the conformal factor dynamics in $D=6$. Accepting the proposal
that higher-derivative dimensionless terms in the anomaly-induced effective
action may be dropped, we obtain a superrenormalizable (like in $D=4$)
effective theory for the conformal factor. The one-loop analysis of this theory
gives the anomalous scaling dimension for the conformal factor and provides a
natural mechanism to solve the cosmological constant problem.
