  We examine the constraints cosmological observations can place on any
trans-Planckian corrections to the primordial spectrum of perturbations
underlying the anisotropies in the Cosmic Microwave Background. We focus on
models of trans-Planckian physics which lead to a modulated primordial
spectrum. Rather than looking at a generic modulated spectrum, our calculations
are based on a specific model, and are intended as a case study for the sort of
constraints one could hope to apply on a well-motivated model of
trans-Planckian physics. We present results for three different approaches -- a
grid search in a subset of the overall parameter space, a Fisher matrix
estimate of the likely error ellipses, and a Monte Carlo Markov Chain fit to a
simulated CMB sky. As was seen in previous analyses, the likelihood space has
multiple peaks, and we show that their distribution can be reproduced via a
simple semi-analytic argument. All three methods lead to broadly similar
results. We vary 10 cosmological parameters (including two related to the
trans-Planckian terms) and show that the amplitude of the tensor perturbations
is directly correlated with the detectability of any trans-Planckian
modulation. We argue that this is likely to be true for any trans-Planckian
modulation in the paradigm of slow-roll inflation. For the specific case we
consider, we conclude that if the tensor to scalar ratio, $r \sim 0.15$, the
ratio between the inflationary Hubble scale $H$, and the scale of new physics
$M$ has to be on the order of 0.004 if the modulation is detectable at the
2$\sigma$ level. For a lower value of $r$, the bound on $H/M$ becomes looser.
