The deformation of Newtonian droplets with zero interfacial tension in a Newtonian matrix is studied in simple shear flow for viscosity ratios ranging from 0.095 to 10.29. The experiments use a counter-rotating Couette apparatus driven by independent servo motors, with a control scheme that keeps the droplet centered under a video camera. Droplet deformation is measured by analyzing the video images, using the method of moments. Both the matrix and the droplet are silicons oils, and the droplet contains a fluorescent dye. Low-viscosity droplets stretch monotonically, while higher viscosity droplets may stretch, wobble, or tumble. The theory of Wetzel and Tucker (2001) for ellipsoidal droplets with zero interfacial tension is compared to the data, by adjusting those portions of the initial shape and orientation that are not observable in the experiment. The agreement is excellent in all cases, requiring only that the initial droplet shape be close to an ellipsoid. (C) 2001 The Society of Rheology.