Acoustic waveguides $\Omega^\eps\subset{\mathbb R}^d$. $d\geq3$ with
the constant cross-section $\omega$ but a curved axis will be constracted
such that
the Neumann Laplacian gets eigenvalues embedded into the first interval of
the continuous
spectrum. Two different approaches will be presented. The first one wiorks
in the case of double
symmetry of $\omega$ and uses artificial boundary conditions and variational
methods.
The second one is based on asymptotic analysis of an auxiliary object,
namely the augmented scattering
matrix which provides a sufficient condition for the existence of trapped
waves. In the second case
the cuvature of the axis is assumed to be small, of order $\eps<<1$, but in
the first case can be arbitrary.