Sen's Liberal Paradox has received a good deal of attention in the literature. However, it is worth re-opening the discussion since the solutions offered so far have serious problems and since there is more to say about the nature of the problem displayed by the Liberal Paradox. I propose a new solution to the paradox in the following sense: First, I argue that its range of applicability is not very broad. Second, there is nothing paradoxical about a conflict of the (...) principles involved in the Liberal Paradox. (Nagel's thesis of the ``fragmentation of value'' is important to make this point.) Third, I make a recommendation about how to remove conflicts when they occur in a restricted class of cases. For the other cases, no recommendation of similar appeal is available. But in the light of the first point, the availability of a generally applicable recommendation was not to be expected. (shrink)