We study co-rotational wave maps from (3 + 1)-Minkowski space to the three-sphere S-3. It is known that there exists a countable family {f(n)} of self-similar solutions. We investigate their stability under linear perturbations by operator theoretic methods. To this end we study the spectra of the perturbation operators, prove well-posedness of the corresponding linear Cauchy problem and deduce a growth estimate for solutions. Finally, we study perturbations of the limiting solution which is obtained from f(n) by letting n -> infinity.