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Breast lesion visibility in static strain imaging ultimately is noise limited. When correlation and related techniques are applied to estimate local displacements between two echo frames recorded before and after a small deformation, target contrast increases linearly with the amount of deformation applied. However, above some deformation threshold, decorrelation noise increases more than contrast such that lesion visibility is severely reduced. Multicompression methods avoid this problem by accumulating displacements from many small deformations to provide the same net increase in lesion contrast as one large deformation but with minimal decorrelation noise. Unfortunately, multicompression approaches accumulate echo noise (electronic and sampling) with each deformation step as contrast builds so that lesion visibility can be reduced again if the applied deformation increment is too small. This paper uses signal models and analysis techniques to develop multicompression strategies that minimize strain image noise. The analysis predicts that displacement variance is minimal in elastically homogeneous media when the applied strain increment is 0.0035. Predictions are verified experimentally with gelatin phantoms. For in vivo breast imaging, a strain increment as low as 0.0015 is recommended for minimum noise because of the greater elastic heterogeneity of breast tissue.