ABSTRACT: States near the vacuum having (n)<<1 are used for the precision determination of a phase shift. When this phase shift is sampled by enough of these near-vacuum states, its size may be extracted via data analysis. We calculate the achievable sensitivity of such schemes when we are limited in our resources to a mean total number of quanta N_tot. We study in detail some examples of these near-vacuum schemes and show that in the absence of loss or noise their sensitivity approaches that of squeezed-state interferometry