Ever since Rawls published The Theory of Justice (1971/2009), the theory itself, along with many of its components, have been subject to intense debate. Both the "original position" and the "veil of ignorance" have been argued to be too unrealistic since the restriction on information makes it impossible to apply in the real world. Furthermore, it is argued that this restriction is too extensive, in that it excludes information that is necessary for making a just decision, and thus, that it contravenes fundamental egalitarian principles, making it less just than it should be. However, there still seems to be something appealing about the concept of the veil of ignorance and results from various experiments that have used it have shown results that indicate it has an effect, which implies that the concept might have some use after all. In this paper, I will argue for a modified version of Rawls' veil of ignorance that, while limited in its available applications, might both serve a practical use in society to increase justice and have a low risk of obtaining inegalitarian results. I will do this by first summarizing Rawls' theory of justice with a focus on his veil of ignorance. Second, I will present and discuss the critiques from various philosophers. Third, I will discuss the implications of several experiments that make use of the veil of ignorance, including the issue that these experiments are 'one-shot', or single iteration, experiments. Finally, I will detail my version of the veil of ignorance and explain why it both meets the critiques of the original veil of ignorance and could potentially serve a practical use in society.