In this paper, we present a solution to the problem of achieving both decoupling of an output of a nonlinear system from (nonlinear) disturbances and uniform BIBO stability of the closed-loop state equations driven by the disturbances. While this involves asymptotic stabilization of the nonlinear system as a special case, BIBO stability entails much more. For example, in the context of DDP, under a fairly mild additional ssumption, BIBO stabilization will imply that the system is minimum phase, in the sense that the nonlinear zero dynamics are globally asymptotically stable. Our main result is a substantial partial converse asserting, modulo technicalities concerning completeness of vector fields, that when DDP is solvable, when the disturbance channels are bounded and when the system is exponentially minimum phase, DDP with uniform BIBO stability (DDPS) can be achieved via state feedback. We remark that our solution of DDPS is valid not just for initial data at an equilibrium, but for a priori bounded sets of initial data. The methods used are special cases of general techniques for the analysis and design of nonlinear feedback systems which will appear elsewhere in a forthcoming series of papers. The result is illustrated for the case of a two generator, lossless PV power system.