  We study the finite convergence of iterative methods for solving convex
feasibility problems. Our key assumptions are that the interior of the solution
set is nonempty and that certain overrelaxation parameters converge to zero,
but with a rate slower than any geometric sequence. Unlike other works in this
area, which require divergent series of overrelaxations, our approach allows us
to consider some summable series. By employing quasi-Fej\'{e}rian analysis in
the latter case, we obtain additional asymptotic convergence guarantees, even
when the interior of the solution set is empty.
