We present a new strategy for fitting the structure and kinematics of the H I in edge-on galaxies using a fit to the terminal-velocity channel maps of a H I data cube. The strategy can deal with self-absorbing H I gas and the presence of warps. The method is first tested on a series of models. We demonstrate that fitting optically thin models to real galaxies will lead to an overestimation of the thickness and velocity dispersion, and to a serious underestimation of the H I face-on column densities. We subsequently fit both self-absorption and optically thin models to the H I data of six edge-on galaxies. In three of these, we have also measured the velocity dispersion. On average, 27 ± 6 per cent of the total H I mass of edge-on galaxies is hidden by self-absorption. This implies that the H I mass, thickness and velocity dispersion of galaxies is typically underestimated in the literature.