MEMS devices (40) using etched cavities (42) are desirably formed using multiple etching steps. Preliminary cavities (20) formed by locally anisotropic etching to nearly the final depth have irregular (46) sidewalls (44) and steep and/or inconsistent sidewall (44) to bottom (54) intersection angles (48). This leads to less than desired cavity diaphragm (26) burst strengths. Final cavities (42) with smooth sidewalls (50), smaller and consistent sidewall (50) to bottom (54) intersection angles (58), and having more than doubled cavity diaphragm (26) burst strengths are obtained by treating the preliminary cavities (20) with TMAH etchant, preferably relatively dilute TMAH etchant. In a preferred embodiment, a cleaning step is performed between the etching step and the TMAH treatment step to remove any anisotropic etching by-products present on the preliminary cavities' (20) initial sidewalls (44). The multi-step cavity etching procedure is especially useful for forming robust MEMS pressure sensors, but is applicable to any type of MEMS device.