  In a recent preprint of F. Gouvea and N. Yui (see arXiv:0902.1466) a detailed
account is given of a patching argument due to Serre that proves that the
modularity of all rigid Calabi-Yau threefolds defined over the rationals
follows from Serre's modularity conjecture. In this note (a letter to N. Yui)
we give an alternative proof of this implication. The main difference with
Serre's argument is that instead of using as main input residual modularity in
infinitely many characteristics we just require residual modularity in a
suitable characteristic. This is combined with effective Cebotarev.
