Recent demonstrations of both heat-to-electricity energy conversion devices and electrocaloric devices based on first-order ferroelectric phase transformations identify the lowering of hysteresis and cyclic reversibility of the transformation as enabling criteria for the advancement of this technology. These demonstrations, and recent studies of the hysteresis of phase transformations in oxides, show that satisfying conditions of supercompatibility can be useful for lowering hysteresis, but with limitations for systems with only a few variants of the lower symmetry phase. in particular, it is widely accepted that in a classic cubic-to-tetragonal phase transformation, with only three tetragonal variants having only six twin systems, tuning for improved crystallographic compatibility will be of limited value. This work shows that, on the contrary, the tuning of lattice parameters in Ba(Ti 1-x Zr x)o 3 for improved crystallographic compatibility, even at low doping levels of Zr (x ≤ 0.027), give significant improvement of transformation and ferroelectric energy conversion properties. Specifically, the transformation hysteresis is lowered by 25%, and the maximum value of the polarization/temperature ratio dP/dT at the phase transformation is increased by 10%. Recently, new devices for the direct (i.e. without a separate electrical generator) conversion of heat to electricity have emerged based on first order ferroelectric phase transformations 1,2. These devices are designed to harvest energy from small temperature differences in the environment, from industrial sources, or from computers and digital devices. From a materials science perspective the main challenges facing the development of this technology, as identified in these papers, are the management of leakage, the cyclic reversibility of the transformation, and the minimization of hysteresis. The latter, which is of interest here, is identified as the main source of loss in this application. In metals, most prominently in TiNi-based shape memory alloys, an understanding of the factors affecting reversibility and hysteresis is quite far advanced. For a high cyclic reversibility it is well-accepted 3 that having a high to low symmetry transformation with a group-subgroup relation, small volume change, and the existence of many low energy austenite/martensite interfaces are desirable. As an example of the influence of these factors, no reasonable shape memory effect has been demonstrated using any metal with a cubic-to-tetragonal phase transformation in polycrystalline form. As demonstrated in slightly Ni-rich TiNi alloys, a fine array of suitable coherent precipitates is also highly desirable, as is a fine, but not too fine, grain size 3,4. The most dramatic improvements in cyclic reversibility, and also thermal hysteresis, have been achieved by tuning the lattice parameters to satisfy conditions of supercompatibility 5-8. Supercompatibility refers to special conditions on the lattice parameters that eliminate stressed transition layers between phases. The simp...