The problem of optimal reachability set computation with alternate performance indices and independent parameters for smooth value functions is motivated and examined. A General Independent Parameter Hamilton Jacobi Bellman PDE formulation is derived and an independent parameter mapping function is defined. Performance index metric properties are leveraged to define Generalized Metric Range Sets. For Newtonian systems it is shown that singular independent parameter mappings can be circumvented using constants of motion. Finally, the motivating problem is solved using the central results of this technical note to generate free-time, Delta v-constrained orbital metric range sets.