  In this proceeding, we present the results of a semi-analytic study of CDM
substructure as a function of the primordial power spectrum. We apply our
method to several tilted models in the LCDM framework with n=0.85-1.1,
sigma_8=0.65-1.2 when COBE normalized. We also study a more extreme, warm dark
matter-like spectrum that is sharply truncated below a scale of 10^10 h^-1
Msun. We show that the mass fraction of halo substructure is not a strong
function of spectral slope, so it likely will be difficult to constrain tilt
using flux ratios of gravitationally lensed quasars. On the positive side, all
of our CDM-type models yield projected mass fractions in good agreement with
strong lensing estimates: f \sim 1.5% at M \sim 10^8 Msun. The truncated model
produces a significantly smaller fraction, f \lsim 0.3%, suggesting that warm
dark matter-like spectra may be distinguished from CDM spectra using lensing.
We also discuss the issue of dwarf satellite abundances, with emphasis on the
cosmological dependence of the map between the observed central velocity
dispersion of Milky Way satellites and the maximum circular velocities of their
host halos. In agreement with earlier work, we find that standard LCDM
over-predicts the estimated count of Milky Way satellites at fixed Vmax by an
order of magnitude, but tilted models do better because subhalos are less
concentrated. Interestingly, under the assumption that dwarfs have isotropic
velocity dispersion tensors, models with significantly tilted spectra (n \lsim
0.85, sigma_8 \lsim 0.7) may under-predict the number of large Milky Way
satellites with Vmax \gsim 40 km/s.
