Sonoelastography is an ultrasonic technique that provides qualitative and quantitative images of tissue elasticity. Even though the Kasai variance estimator is a key part of the sonoelastographic image formation, there are no studies that demonstrate that its performance using discrete time signals and finite sized ensemble lengths is optimal. In this work, the influence of the selection of acquisition parameters (pulse repetition frequency or PRF, vibration frequency, and ensemble length) on the quality of the elastograms is studied. Simulations are carried out to define the optimal PRF and ensemble length given a vibration frequency in order to avoid artifacts which can severely degrade image quality. This empirical criterion is supported by sonoelastography experiments performed using two commercial scanners, where the variability increased from 4% to 42% at the worst selection of acquisition parameters. Although a further mathematical proof of the empirical findings is required, these results suggest that careful selection of PRF, vibration frequency and ensemble lengths is required to ensure unbiased sonoelastograms.