The systematic tuning of the lattice parameters to achieve improved kinematic compatibility between phases is a broadly effective strategy for improving the reversibility, and lowering the hysteresis, of solid-solid phase transformations. Here, "kinematic compatibility" refers to the fitting together of the phases. We present an apparently paradoxical example in which tuning to near perfect compatibility in (Zr/Hf)O2-(YNb)O4 results in a high degree of irreversibility, as manifested in explosive or "weeping" behavior on cooling through the tetragonal-to-monoclinic phase transformation. In the case of weeping the polycrystal slowly and steadily falls apart at the grain boundaries. These effects occur without chemical change. Finally, tuning to satisfy a condition we term the equidistance condition results in reversible behavior with the lowest hysteresis in this system. We give evidence that all these observations are explained by a more careful analysis of compatibility of the polycrystal, accounting for sample shape. These results show that an extreme diversity of behaviors, from reversible to explosive, is possible in a chemically homogeneous system by manipulating conditions of compatibility in unexpected ways. They provide critical concepts underlying the current search for a shape memory oxide ceramic.