  We consider Schr\"odinger operators with potentials satisfying a generalized
bounded variation condition at infinity and an $L^p$ decay condition. This
class of potentials includes slowly decaying Wigner--von Neumann type
potentials $\sin(ax)/x^b$ with $b>0$. We prove absence of singular continuous
spectrum and show that embedded eigenvalues in the continuous spectrum can only
take values from an explicit finite set. Conversely, we construct examples
where such embedded eigenvalues are present, with exact asymptotics for the
corresponding eigensolutions.
