Thick (i.e., greater than two microns), fine-grained, low-stress tungsten MEMS structures are fabricated at low temperatures, particularly for so-called “MEMS last” fabrication processes (e.g., when MEMS structures are fabricated after electronic circuitry is fabricated). Means for very accurately etching structural details from the deposited tungsten layer and for strongly and stably anchoring the tungsten layer to an underlying substrate are disclosed. Also, means for removing a sacrificial layer underlying the mobile tungsten layer without damaging the tungsten or allowing it to be drawn down and stuck by surface tension is disclosed.