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Although a wide variety of sensitivity analysis methods for additive value models appear in the literature, the most commonly used and easily understood is one-way sensitivity analysis. We address concerns from practice with this traditional method and build the mathematical foundation for a new and robust one-way sensitivity analysis approach that enables the decision maker(s) to gain a greater ownership of the model. A traditional one-way sensitivity analysis varies one attribute weight while keeping all others proportionally constant; although useful, it also has limitations, particularly in group decision making. Our proposed methodology, customizable one-way sensitivity analysis (COSA), retains the simplicity of the traditional method but extends it to a more powerful form. COSA allows the decision maker(s) to tailor the sensitivity analysis to the desired decision context by assigning weight coefficients of elasticity to the attribute weights. These parameters let the decision maker choose how the adjusted weight change is distributed throughout the model. Furthermore, we provide a detailed discussion about performing sensitivity analysis on complex hierarchies with more than one tier and include an applied example to demonstrate COSA's usefulness. Overall, a consistent standard for the one-way sensitivity analysis of additive value models is provided for the decision analysis community.