Despite rising real incomes, the number of uninsured American workers and their dependents has not fallen appreciably. Policymakers in both political parties have considered the use of tax credits to encourage the purchase of private insurance coverage. This study analyzes the effects of a variety of forms of tax credits, especially for workers whose incomes place them above the poverty line but below the median family income -- a group in which the vast majority of the uninsured are to be found. The authors' conclusions differ from more conventional analyses in two ways. First, they find plausible effects on the numbers of uninsured persons that are larger than those of other studies. Second, they explore the distinction between the "cost" to the federal government of tax credits and the more relevant measures of tax credits' effects on aggregate economic welfare and cost to the economy. Nevertheless, they still find, as do most other analysts, that modest subvsidies will have little effect in reducing the number of the uninsured. For a given amount "spent" on credits, a key tradeoff exists between the breadth of the reduction in the uninsured and the depth of the increase in the coverage they take. While it is unlikely that the number of uninsured will ever be literally zero, the authors believe that carefully designed tax credits can both reduce the numbers of uninsured and improve the equity of tax treatment of the insured.