It is commonly contended by the political right that freedom and equality are mutually incompatible values. This 'incompatibility argument' can be characterized as positing a trade-off between freedom and equality, such that the more a society realizes of one, the less it is able to realize of the other. Talk of trade-offs between values implies the possibility that they can be subjected to quantitative analysis, and in order to make sense of the trade-off interpretation of the incompatibility argument I identify quantifiable conceptions of freedom and equality. The incompatibility argument invokes negative freedom and equality of outcome. Consequently it is often resisted by endorsement of alternative conceptions of these values like positive freedom or equality of opportunity. Refraining from this strategy, I aim to show that for those committed to both negative freedom and equality of outcome the outlook is not as bleak as the incompatibility argument would seem to suggest. This is because the traditional picture ignores the context in which the trade-off between freedom and equality takes place, namely, the widespread privatization of resources. I argue that in addition to the advertised trade-off between freedom and equality, each of these values also trades off against the extent to which private property rights are enshrined. As above, for trade-offs to take place between private property and other social goals it must be possible to quantify private property, and I seek to show that such quantification can be achieved. If my analysis is successful we will then be faced with three trade-offs: freedom vs. equality, freedom vs. private property, and equality vs. private property. By integrating these three trade-offs into a single three-dimensional model I aim to present a more informative account of the relationships between the three goals. The extent to which freedom and equality trade-off against one another is itself determined in part by the extent to which a society realizes private property. As a result, by curbing or abolishing private property rights more freedom can be secured alongside greater equality.