Delay budget is an excess delay that each component of a design can tolerate under a given timing constraint. Delay budgeting has been widely exploited to improve the design quality. This paper presents the idea of incrementally re-assigning the delay budgets allotted to different components of a design, which leads to avoiding the re-execution of the intensive budget assignment procedure in each iteration of the tools. Given a budgeting solution and a local change, our approach can re-assign the budget values such that the timing constraints are met. More importantly, it only explores the components locally, which preserves its incremental nature. General sufficient conditions have been presented under which, our approach is provably effective. Experimental results on converting non-integral budgeting assignments to integral ones, advocate our technique's efficiency. The budget assignments have been used to map a number of applications to an FPGA platform. The results have been ...