Uncertainty is an unavoidable aspect of engineering systems and will often degrade system performance or perhaps even lead to system failure. As a result, uncertainty must be considered as a part of the design process for all real-world engineering systems. The presence of reducible uncertainty further complicates matters as designers must not only account for the degrading effects of uncertainty but must also determine what levels of uncertainty can be considered as acceptable. For these reasons, methods for determining and effectively mitigating the effects of uncertainty are necessary for solving engineering design problems. This dissertation presents several new methods for use in the design of engineering systems under interval input uncertainty. These new approaches were developed over the course of four interrelated research thrusts and focused on the overall goal of extending the current research in the area of sensitivity analysis based design under reducible interval uncertainty. The first research thrust focused on developing an approach for determining optimal uncertainty reductions given multi-disciplinary engineering systems with multiple output functions at both the system and sub-system levels. The second research thrust extended the approach developed during the first thrust to use uncertainty reduction as a means for both reducing output variations and simultaneously ensuring engineering feasibility. The third research thrust looked at systems where uncertainty reduction alone is insufficient for ensuring feasibility and thus developed a sensitivity analysis approach that combined uncertainty reductions with small design adjustments in an effort to again reduce output variations and ensure feasibility. The fourth and final research thrust looked to relax many of the assumptions required by the first three research thrusts and developed a general sensitivity analysis inspired approach for determining optimal upper and lower bounds for reducible sources of input uncertainty. Multi-objective optimization techniques were used throughout this research to evaluate the tradeoffs between the benefits to be gained by mitigating uncertainty with the costs of making the design changes and/or uncertainty reductions required to reduce or eliminate the degrading effects of system uncertainty most effectively. The validity of the approaches developed were demonstrated using numerical and engineering example problems of varying complexity.