The most common mutation system of Welsh, soft mutation, affects among other elements the object of a finite verb. This is often known as direct object mutation (DOM). Objects have accusative Case in many languages. Hence, it is natural to consider the possibility that DOM is a manifestation of accusative Case, and this has been proposed by a number of people. There is evidence, however, that this idea is both too strong and too weak. It predicts soft mutation where it does not in fact occur, and there are a number of instances of soft mutation which appear to form a natural class with DOM but cannot plausibly be analyzed as a manifestation of accusative Case. A widely discussed alternative to a Case-based view of DOM is one in which DOM is triggered by a preceding phrase of some kind. This approach looks quite promising. However, it does not fit readily into the Principles and Parameters framework. It seems, then, that DOM poses a major challenge for this framework.