  We consider a class of inflationary models with small oscillations imprinted
on an otherwise smooth inflaton potential. These oscillations are manifest as
oscillations in the power spectrum of primordial perturbations, which then give
rise to oscillating departures from the standard cosmic microwave background
power spectrum. We show that current data from the Wilkinson Microwave
Anisotropy Probe constrain the amplitude of a sinusoidal variation in the
inflaton potential to have an amplitude less than 3 x 10^{-5}. We anticipate
that the smallest detectable such oscillations in Planck will be roughly an
order of magnitude smaller, with slight improvements possible with a
post-Planck cosmic-variance limited experiment.
