The two ellipsometric parameters of an isotropic sample can be measured with simplified polarimetry setups that acquire a minimum number of four intensity measurements. However, these measurements are perturbed by noise, and the measurement strategy has to be optimized in order to limit noise propagation. We determine two different measurement strategies that are optimal in the presence of both white Gaussian additive noise and Poisson shot noise. The first one involves a polarization state generator (PSG) with a single state of polarization and a polarization state analyzer (PSA) with four states, and in the second one, both PSG and PSA have two states. The total estimation variances obtained with both strategies are demonstrated to be minimal, of equal values and independent of the ellipsometric parameters to be measured. They are based on simple optical elements and have the potential to simplify and accelerate ellipsometric measurements.