This paper describes a detailed examination of the effects of a relatively small pulsed deuterium gas puff on the edge plasma and edge turbulence in NSTX. This gas puff caused little or no change in the line-averaged plasma density or total stored energy, or in the edge density and electron temperature up to the time of the peak of the gas puff. The radial profile of the Dα light emission and the edge turbulence within this gas puff did not vary significantly over its rise and fall, implying that these gas puffs did not significantly perturb the local edge plasma or edge turbulence. These measurements are compared with modeling by DEGAS 2, UEDGE, and with simplified estimates for the expected effects of this gas puff.