Lateral DMOS devices having improved drain contact structures and methods for making the devices are disclosed. A semiconductor device comprises a semiconductor substrate; an epitaxial layer on top of the substrate; a drift region at a top surface of the epitaxial layer; a source region at a top surface of the epitaxial layer; a channel region between the source and drift regions; a gate positioned over a gate dielectric on top of the channel region; and a drain contact trench that electrically connects the drift layer and substrate. The contact trench includes a trench formed vertically from the drift region, through the epitaxial layer to the substrate and filled with an electrically conductive drain plug; electrically insulating spacers along sidewalls of the trench; and an electrically conductive drain strap on top of the drain contact trench that electrically connects the drain contact trench to the drift region.