  The fundamental quasinormal modes of black holes in higher-derivative gravity
given by the Einstein-Weyl action are known to be moderately corrected by the
Weyl term. Here we will show that the first several overtones are highly
sensitive to even a relatively small Weyl correction, which might be important
when representing the earlier stage of the black hole ringdown. In addition, we
have solved the problem related to the analytical parametrized approximation of
the numerical black hole solution in the Einstein-Weyl theory: In some range of
parameters the approximation for the metric developed up to the third order
leads to the unusual highly nonmonotonic behavior of the frequencies. We have
shown that this problem can be solved via the extension of the parametrization
of the metric to higher orders until reaching the regime when the frequencies
do not change with further increasing of the order.
