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.