Reduction in the amount of shear used in shearing speckle interferomtery is desirable in applications where multiple wavelength measurements are required. The limit to this reduction, however, is determined by the statistical phase variance effect and imaging aberrations. Although the latter effect has been mentioned, it has, hitherto, not been studied in detail. In this paper, wavefront aberrations are simulated using uniform deviate random number generators on the computer and the additive noise analyzed at various nucleation, fluctuation, correlation length and shear levels. It is established that while larger nucleation, correlation length and fluctuation levels all contribute to an increase in the overall noise in the speckle image, only the correlation length imposes a limit on shear reduction in shearing speckle interferometry.