In a low Morton number (M) regime, the stability of a single drop rising in an immiscible viscous liquid is experimentally and computationally examined for varying viscosity ratio η (the viscosity of the drop divided by that of the suspending fluid) and varying Eötvös number (Eo). Three-dimensional computations, rather than three-dimensional axisymmetric computations, are necessary since non-axisymmetric unstable drop behaviour is studied. The computations are performed using the sharp-interface coupled level-set and volume-of-fluid (CLSVOF) method in order to capture the deforming drop boundary. In the lower η regimes, η = 0.02 or 0.1, and when Eo exceeds a critical threshold, it is observed that a rising drop exhibits nonlinear lateral/tilting motion. In the higher η regimes, η = 0.1, 1.94, 10 or 100, and when Eo exceeds another critical threshold, it is found that a rising drop becomes unstable and breaks up into multiple drops. The type of breakup, either 'dumbbell', 'intermediate' or 'toroidal', depends intimately on η and Eo.