The shortest path (SP) and shortest paths tree (SPT) problems arise both as direct applications and as subroutines of overlay algorithms solving more complex problems such as the constrained shortest path (CSP) or the constrained minimum Steiner tree (CMST) problems. Often, such algorithms do not use the result of an SP subroutine if its total cost is greater than a given bound. For example, for delay-constrained problems, paths resulting from a least-delay SP run and whose delay is greater than the delay constraint of the original problem are not used by the overlay algorithm to construct its solution. As a result of the existence of these bounds, and because the Dijkstra SP algorithm discovers paths in increasing order of cost, we can terminate the SP search earlier, i.e., once it is known that paths with a greater total cost will not be considered by the overlay algorithm. This early termination allows to reduce the runtime of the SP subroutine, thereby reducing the runtime of the overlay algorithm without impacting its final result. We refer to this adaptation of Dijkstra for centralized implementations as bounded Dijkstra (BD). On the example of CSP algorithms, we confirm the usefulness of BD by showing that it can reduce the runtime of some algorithms by 75% on average.