© 2019, The Author(s). Reducing parameter spaces via exploiting symmetries has greatly accelerated and increased the quality of electronic-structure calculations. Unfortunately, many of the traditional methods fail when the global crystal symmetry is broken, even when the distortion is only a slight perturbation (e.g., Jahn-Teller like distortions). Here we introduce a flexible and generalizable parametric relaxation scheme and implement it in the all-electron code FHI-aims. This approach utilizes parametric constraints to maintain symmetry at any level. After demonstrating the method’s ability to relax metastable structures, we highlight its adaptability and performance over a test set of 359 materials, across 13 lattice prototypes. Finally we show how these constraints can reduce the number of steps needed to relax local lattice distortions by an order of magnitude. The flexibility of these constraints enables a significant acceleration of high-throughput searches for novel materials for numerous applications.