The classic problem of global register allocation is treated in a heuristic and practical manner by adopting the notion of priorities in node-coloring. The assignment of priorities is based on estimates of the benefits that can be derived from allocating individual quantities in registers. Using the priorities, the exponential coloring process can be made to run in linear time. Since the costs involved in register allocation are taken into account, the algorithm does not over-allocate. The algorithm can be parameterized to cater to different fetch characteristics and register configurations among machines. Measurements indicate that the register allocation scheme is effective on a number of target machines. The results confirm that, using priority-based coloring, global register allocation can be performed practically and efficiently.