Most economists agree that the difficulties of targeting minimum wage increases to low-income families make such increases ineffective tools for reducing poverty. This paper provides estimates of the impact of minimum wage increases on the poverty gap and the number of poor families, and shows which factors are barriers to decreasing poverty through minimum wage increases. A model was developed for simulating the poverty reducing effects of minimum wage increases using wage, employment, hours, and poverty status data from the March 1987 Current Population Survey. Findings indicate that an increase of the minimum wage to $4.35 per hour has a much larger poverty reducing effect than previous research suggests. If accompanied by full coverage and compliance, such an increase would reduce the poverty gap by 13 percent, and the number of poor families with low-wage workers would decrease by nine percent. However, the resulting unemployment of some workers could reduce the poverty-reducing effects. Ten tables of statistical data are included. The appendix contains two additional tables showing a sensitivity analysis of the effects of changes in the minimum wage, with full coverage and compliance, and with the coverage and compliance unchanged. (FMW)