Biological membrane fission requires protein-driven stress. The guanosine triphosphatase (GTPase) dynamin builds up membrane stress by polymerizing into a helical collar that constricts the neck of budding vesicles. How this curvature stress mediates nonleaky membrane remodeling is actively debated. Using lipid nanotubes as substrates to directly measure geometric intermediates of the fission pathway, we found that GTP hydrolysis limits dynamin polymerization into short, metastable collars that are optimal for fission. Collars as short as two rungs translated radial constriction to reversible hemifission via membrane wedging of the pleckstrin homology domains (PHDs) of dynamin. Modeling revealed that tilting of the PHDs to conform with membrane deformations creates the low-energy pathway for hemifission. This local coordination of dynamin and lipids suggests how membranes can be remodeled in cells.