A wide diversity of bilayer membranes, from those with hundreds of lipids (e.g., vacuoles of living yeast cells) to those with very few (e.g., artificial vesicles) phase separate into micron-scale liquid domains. The number of components required for liquid-liquid phase separation has been perplexing: only two should be necessary, but more are required except in extraordinary circumstances. What minimal set of molecular characteristics leads to liquid-liquid phase separation in bilayer membranes? This question inspired us to search for single, joined "sterol-lipid" molecules to replace both a sterol and a phospholipid in membranes undergoing liquid-liquid phase separation. By producing phase-separating membranes with only two components, we mitigate experimental challenges in determining tie-lines and in maintaining constant chemical potentials of lipids.