We prove that if (X, U) has a Hausdorff *-compactification, then there is a proximity rU on X such that the *-compactification of (X, U) is equivalent to the Smirnov compactification of (X, rU). Furthermore, the Smirnov compactification of (X, rU) is the greatest Hausdorff (quasi-uniform) compactification of (X, U). We also show that if, in addition, (X, U) is transitive, then the Smirnov compactification of (X, rU) is a Wallman type compactification.