  We consider Dirichlet Laplacians on straight strips in R^2 or layers in R^3
with a weak local deformation. First we generalize a result of Bulla et al. to
the three-dimensional situation showing that weakly coupled bound states exist
if the volume change induced by the deformation is positive; we also derive the
leading order of the weak-coupling asymptotics. With the knowledge of the
eigenvalue analytic properties, we demonstrate then an alternative method which
makes it possible to evaluate the next term in the asymptotic expansion for
both the strips and layers. It gives, in particular, a criterion for the
bound-state existence in the critical case when the added volume is zero.
