  Recently is has been suggested that the dearth of small halos around the
Milky Way arises due to a modification of the primordial power spectrum of
fluctuations from inflation. Such modifications would be expected to alter the
formation of structure from bottom-up to top-down on scales near where the
short-scale power has been suppressed. Using cosmological simulations we study
the effects of such a modification of the initial power spectrum. While the
halo multiplicity function depends primarily on the linear theory power
spectrum, most other probes of power are more sensitive to the non-linear power
spectrum. Collapse of large-scale structures as they go non-linear regenerates
a ``tail'' in the power spectrum, masking small-scale modifications to the
primordial power spectrum except at very high-z. Even the small-scale
(k>2h/Mpc) clustering of the Ly-alpha forest is affected by this process, so
that CDM models with sufficient power suppression to reduce the number of 10^10
Msun halos by a factor of about 5 give similar Ly-alpha forest power spectrum
results. We conclude that other observations that depend more directly on the
number density of collapsed objects, such as the number of damped Ly-alpha
systems, or the redshift of reionization may provide the most sensitive tests
of these models.
