We have combined two epochs of Hubble Space Telescope WFPC2 imaging data with ground-based expansion velocities to determine distances to three planetary nebulae (NGC 6578, NGC 6884, and IC 2448). We used two variants of the expansion parallax technique--a gradient method and a magnification method--to determine the distances. The results from the two methods agree to within the errors. A fourth nebula was included in the study (NGC 6891), but the expansion was too small to determine the distance, and only a lower limit was obtained. This is the first paper in a series which will examine at least 24 nebulae in total.