  We study large classes of renormalization group flows, driven by scalar
expectation values or mesonic superpotential terms, away from the conformal
fixed points of the 4d supersymmetric gauge theories with $ADE$-type
superpotentials. The $a$-maximization procedure allows us to compute the $R$
charges and to check the $a$-theorem conjecture. For a theory obtained by
Higgsing the $D_{k+2}$ theory, we use the magnetic dual description proposed by
Brodie to determine the parameter region where the resulting theory is at a
non-trivial conformal fixed point.
