  The perturbation theory by L. Ge et al. [Phys. Rev. A 87, 023833] for
transverse-electric polarized modes in weakly deformed microdisks omits terms
related to the variation of the normal derivative of the magnetic field along
the boundary. Here we show that these terms are necessary to accurately
describe microdisks with a strongly winding boundary. In particular, it is
demonstrated that the corrected perturbation theory allows to describe the
counterintuitive phenomenon of Q-factor enhancement due to weak boundary
deformation. We discuss in detail the microflower cavity and the limacon
cavity. Good agreement of the corrected perturbation theory with full numerical
results is observed.
