  The cold dark matter (CDM) model of structure formation, normalized on large
scales, leads to excessive pairwise velocity dispersions on small scales. In an
attempt to circumvent this problem, we study three scenarios (all with
$\Omega=1$) which have more large-scale power and less small-scale power than
the CDM model: 1) an admixture of cold and hot dark matter; 2) cold dark matter
with a non-scale-invariant, power-law primordial power spectrum; and 3) cold
dark matter with coupling of dark matter to a long-range vector field. Despite
the {reduced} small-scale power, when such models are evolved in the nonlinear
regime to large amplitude, the velocities on small scales are actually {\it
increased} over CDM with the same value of $\sigma_8$. This `flip-over', in
disagreement with the expectation from linear perturbation theory, arises from
the nonlinear coupling of the extra power on large scales with shorter
wavelengths. However, due to the extra large-scale power, the recent COBE DMR
results indicate smaller amplitudes for these models, $\sigma_8 \sim 0.5 -
0.7$, than for CDM (for which $\sigma_8 \sim 1.2$). Therefore, when normalized
to COBE on large scales, such models do lead to reduced velocities on small
scales and they produce fewer halos compared with CDM. Quantitatively it seems,
however, that models that produce sufficiently low small-scale velocities fail
to produce an adequate distribution of halos.
