  Let $K$ be an imaginary quadratic field of discriminant less than or equal to
-7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater
than 1. We prove that singular values of certain Siegel functions generate
$K_{(N)}$ over $K$ by extending the idea of our previous work. These generators
are not only the simplest ones conjectured by Schertz, but also quite useful in
the matter of computation of class polynomials. We indeed give an algorithm to
find all conjugates of such generators by virtue of Gee and Stevenhagen.
