  Perturbations of $WD_n$ and $W_3$ conformal theories which generalize the
$(1,2)$ perturbations of conformal minimal models are shown to be integrable by
counting argument. $A_{2n-1,q}^{(2)}$ and $D_{4,q}^ {(3)}$ symmetries of
corresponding S-matrices are conjectured and proved by explicit construction of
conserved nonlocal charges in the $WD_3$ case with the proper quantum group of
symmetry.
