Fluctuations in the shape of amnioserosa (AS) cells during Drosophila dorsal closure (DC) provide an ideal system with which to understand contractile epithelia, both in terms of the cellular mechanisms and how tissue behaviour emerges from the activity of individual cells. Using quantitative image analysis we show that apical shape fluctuations are driven by the medial cytoskeleton, with periodic foci of contractile myosin and actin travelling across cell apices. Shape changes were mostly anisotropic and neighbouring cells were often, but transiently, organised into strings with parallel deformations. During the early stages of DC, shape fluctuations with long cycle lengths produced no net tissue contraction. Cycle lengths shortened with the onset of net tissue contraction, followed by a damping of fluctuation amplitude. Eventually, fluctuations became undetectable as AS cells contracted rapidly. These transitions were accompanied by an increase in apical myosin, both at cell-cell junctions and medially, the latter ultimately forming a coherent, but still dynamic, sheet across cells. Mutants with increased myosin activity or actin polymerisation exhibited precocious cell contraction through changes in the subcellular localisation of myosin. thick veins mutant embryos, which exhibited defects in the actin cable at the leading edge, showed similar timings of fluctuation damping to the wild type, suggesting that damping is an autonomous property of the AS. Our results suggest that cell shape fluctuations are a property of cells with low and increasing levels of apical myosin, and that medial and junctional myosin populations combine to contract AS cell apices and drive DC.