  We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the
boundary condition which is Dirichlet except at the segment of a length $2a$ of
one of the boundaries where it is switched to Neumann. This operator is known
to have a non-empty and simple discrete spectrum for any $a>0$. There is a
sequence $0<a_1<a_2<...$ of critical values at which new eigenvalues emerge
from the continuum when the Neumann window expands. We find the asymptotic
behavior of these eigenvalues around the thresholds showing that the gap is in
the leading order proportional to $(a-a_n)^2$ with an explicit coefficient
expressed in terms of the corresponding threshold-energy resonance
eigenfunction.
