  In our recent paper we gave an efficient algorithm to calculate "small"
solutions of relative Thue equations (where "small" means an upper bound of
type $10^{500}$ for the sizes of solutions). Here we apply this algorithm to
calculating power integral bases in sextic fields with an imaginary quadratic
subfield and to calculating relative power integral bases in pure quartic
extensions of imaginary quadratic fields. In both cases the crucial point of
the calculation is the resolution of a relative Thue equation. We produce
numerical data that were not known before.
