What are the minimal requirements to sustain an asymmetric cell cycle? Here we use mathematical modelling and forward genetics to reduce an asymmetric cell cycle to its simplest, primordial components. In the Alphaproteobacterium Caulobacter crescentus, cell cycle progression is believed to be controlled by a cyclical genetic circuit comprising four essential master regulators. Unexpectedly, our in silico modelling predicted that one of these regulators, GcrA, is in fact dispensable. We confirmed this experimentally, finding that ΔgcrA cells are viable, but slow-growing and elongated, with the latter mostly due to an insufficiency of a key cell division protein. Furthermore, suppressor analysis showed that another cell cycle regulator, the methyltransferase CcrM, is similarly dispensable with simultaneous gcrA/ccrM disruption ameliorating the cytokinetic and growth defect of ΔgcrA cells. Within the Alphaproteobacteria, gcrA and ccrM are consistently present or absent together, rather than either gene being present alone, suggesting that gcrA/ccrM constitutes an independent, dispensable genetic module. Together our approaches unveil the essential elements of a primordial asymmetric cell cycle that should help illuminate more complex cell cycles.