Two commonly recommended principles for allocating risk management resources to remediate uncertain hazards are: (1) select a subset to maximize risk-reduction benefits (e.g., maximize the von Neumann-Morgenstern expected utility of the selected risk-reducing activities), and (2) assign priorities to risk-reducing opportunities and then select activities from the top of the priority list down until no more can be afforded. When different activities create uncertain but correlated risk reductions, as is often the case in practice, then these principles are inconsistent: priority scoring and ranking fails to maximize risk-reduction benefits. Real-world risk priority scoring systems used in homeland security and terrorism risk assessment, environmental risk management, information system vulnerability rating, business risk matrices, and many other important applications do not exploit correlations among risk-reducing opportunities or optimally diversify risk-reducing investments. As a result, they generally make suboptimal risk management recommendations. Applying portfolio optimization methods instead of risk prioritization ranking, rating, or scoring methods can achieve greater risk-reduction value for resources spent.