In prokaryotes, FtsZ (the filamentous temperature sensitive protein Z) is a nearly ubiquitous GTPase that localizes in a ring at the leading edge of constricting plasma membranes during cell division. Here we report electron cryotomographic reconstructions of dividing Caulobacter crescentus cells wherein individual arc-like filaments were resolved just underneath the inner membrane at constriction sites. The filaments' position, orientation, time of appearance, and resistance to A22 all suggested that they were FtsZ. Predictable changes in the number, length, and distribution of filaments in cells where the expression levels and stability of FtsZ were altered supported that conclusion. In contrast to the thick, closed-ring-like structure suggested by fluorescence light microscopy, throughout the constriction process the Z-ring was seen here to consist of just a few short (approximately 100 nm) filaments spaced erratically near the division site. Additional densities connecting filaments to the cell wall, occasional straight segments, and abrupt kinks were also seen. An 'iterative pinching' model is proposed wherein FtsZ itself generates the force that constricts the membrane in a GTP-hydrolysis-driven cycle of polymerization, membrane attachment, conformational change, depolymerization, and nucleotide exchange.