  We discuss the existence and regularity of periodic traveling-wave solutions
of a class of nonlocal equations with homogeneous symbol of order $-r$, where
$r>1$. Based on the properties of the nonlocal convolution operator, we apply
analytic bifurcation theory and show that a highest, peaked, periodic
traveling-wave solution is reached as the limiting case at the end of the main
bifurcation curve. The regularity of the highest wave is proved to be exactly
Lipschitz. As an application of our analysis, we reformulate the steady reduced
Ostrovsky equation in a nonlocal form in terms of a Fourier multiplier operator
with symbol $m(k)=k^{-2}$. Thereby we recover its unique highest
$2\pi$-periodic, peaked traveling-wave solution, having the property of being
exactly Lipschitz at the crest.
