  We provide a solution to the effectiveness problem in Kohn's algorithm for
generating holomorphic subelliptic multipliers for $(0,q)$ forms for arbitrary
$q$. As an application, we obtain subelliptic estimates for $(0,q)$ forms with
effectively controlled order $\epsilon>0$ (the Sobolev exponent) for domains
given by sums of squares of holomorphic functions (J.J. Kohn called them
"special domains"). These domains are of particular interest due to their
relation with complex and algebraic geometry. Our methods include triangular
resolutions introduced by the authors in their previous work.
