I analyze changes in the target efficiency of the federal minimum wage over the past 25 years. Using static simulation methods I find that minimum wage target efficiency is currently close to its 25‐year peak—of the total monetary benefits generated by a 12% increase in the federal minimum wage, 16.8% would flow to workers in poverty. This exceeds the least target efficient year over this period by 4.7 percentage points and is only 0.6 percentage points below the peak. Furthermore, I find a very strong positive relationship between minimum wage target efficiency and the real federal minimum wage. The implication is that, from an efficiency standpoint, a good time to raise the minimum wage is when it is already high. This discovery raises the possibility that the minimum wage increases the employment of low‐skilled poor individuals relative to the employment of low‐skilled non‐poor individuals. Moreover, this discovery may bolster the rationale for an indexed minimum wage whereby it is prevented from falling to less efficient levels. (JEL J21, J31, J38)