Ultracompact minihalos (UCMHs) have attracted considerable interest as a probe of the primordial power spectrum at small scales. However, previous treatments assumed that halos collapsing at early times possess an extremely steep r^-9/4 density profile. We recently found that UCMHs actually develop shallower r^-3/2 or r^-1 inner profiles depending on the shape of the power spectrum, but these halos are still highly concentrated due to their early formation. I will discuss these results and the factors that set the inner density profile of a dark matter halo. I will also outline the process of deriving power spectrum constraints in this revised picture. Since the formalism can now include halos that collapse at any time, our preliminary revised constraints turn out to be stronger than prior constraints from UCMHs.