Image reconstruction methods employed in horizontal imaging scenarios must provide the best possible reconstructions over a broad range of conditions. In addition to variations in turbulence conditions, these systems must perform when operated by novice users who may lack knowledge regarding the underlying reconstruction algorithms. Systems that maintain their performance under these conditions and are otherwise immune to factors that cause variability in performance are considered to be robust. We evaluate the effect of varying design parameters, such as the number of input frames, inverse filter parameters, and number of phase estimates parametrically. We find that, for most conditions, it is possible to achieve performance near the limit available from these estimators using as few as 15 input frames, the average of 4 estimates of the object phase, and with only approximate knowledge of the imaging conditions. When operated under these conditions, speckle-imagers can be considered robust. In addition to this analysis, the bispectrum and Knox-Thompson methods were compared as alternative phase estimation techniques. We find that the Knox-Thompson phase estimation method is preferred in situations where minimum computation complexity is desired.