We commonly treat feasibility as non-negotiable when it comes to determining what we ought to do and pursue in political life and what justice requires, rejecting highly desirable claims simply because they appear to make infeasible demands and settling for less desirable but feasible alternatives. But what exactly does this preoccupation with feasibility amount to? Is it warranted? And what does it mean for political theory and political practice? In this first book-length treatment of the topic, Nicholas Southwood aims to answer these theoretically complex and practically consequential questions. He argues that there is indeed a valid "Feasibility Requirement" on central normative claims about politics, but that it needs to be fundamentally reinterpreted, by embracing a novel account of feasibility, the scope of the Feasibility Requirement, and its normative basis (that goes beyond the principle that "Ought" Implies "Can"). At the same time, Southwood argues that there remains a crucial role for modes of normative thinking about politics that are not subject to a Feasibility Requirement and that do not aspire to be constrained in this way. The result --what he calls Uncompromising Realism--is a nuanced theory of feasibility and its role in politics that can avoid the dangers of objectionable unworldliness and wishful thinking, on the one hand, and undue concession and compromise, on the other, with far-reaching implications for political theory and practice.