Deformation estimation is the foundation of emerging techniques for imaging the mechanical properties of soft tissues. We present theoretical analysis and experimental results from an investigation of phase-based ultrasonic deformation estimators. Numerous phase-based algorithm variants were tested quantitatively on simulated RF data from uniform scatterer fields, subject to a range of uniform strain deformations. Particular attention is paid to a new algorithm, weighted phase separation, the performance of which is demonstrated in application to in vivo freehand strain imaging. Good results support the theory that underlies the new algorithm, and more generally highlight the factors that should be considered in the design of high performance deformation estimators for practical applications. For context, note that this represents progress with an algorithm class that is suitable for real-time applications, yet has already been shown quantitatively to offer greater accuracy over a wide range of scanning conditions than adaptive companding methods based on correlation coefficient or sum of absolute differences.