Bacterial cells come in a variety of shapes, determined by the stress-bearing cell wall. Though many molecular details about the cell wall are known, our understanding of how a particular shape is produced during cell growth is at its infancy. Experiments on curved Escherichia coli grown in microtraps, and on naturally curved Caulobacter crescentus, reveal different modes of growth: one preserving arc length and the other preserving radius of curvature. We present a simple model for curved cell growth that relates these two growth modes to distinct but related growth rules--"hooplike growth" and "self-similar growth"--and discuss the implications for microscopic growth mechanisms.