Solid-state nanopores are considered a promising tool for the study of biological polymers such as DNA and RNA, due largely to their flexibility in size, potential in device integration and robustness. Here, we show that the precise shape of small nanopores (∼5 nm diameter in 20 nm SiN membranes) can be controlled by using transmission electron microscope (TEM) beams of different sizes. However, when some of these small nanopores are immersed in an aqueous solution, their resistance is observed to decrease over time. By comparing nanopores of different shapes using (scanning) TEM both before and after immersion in aqueous solution, we demonstrate that the stability of small nanopores is related to their three-dimensional geometry, which depends on the TEM beam size employed during pore fabrication. Optimal stability is obtained using a TEM beam size of approximately the same size as the intended nanopore diameter. In addition, we show that thermal oxidation can serve as a means to independently control nanopore size following TEM fabrication. These observations provide key guidelines for the fabrication of stable solid-state nanopores on the scale of nucleic acids and small proteins.