Could an object have only mass and no other property? In giving an affirmative answer to this question, Jonathan Schaffer (2003, pp. 136-8) proposes what he calls ‘the subtraction argument’ for ‘the possibility of free mass’. In what follows, we aim to assess the cogency of this argument in comparison with an argument of the same general form which has also been termed a subtraction argument, namely, Thomas Baldwin’s (1996) subtraction argument for metaphysical nihilism, which is the claim that there might have been no concrete objects. The comparison will be instructive because Baldwin’s argument has been the subject of considerable recent debate (of particular relevance for current purposes are Paseau 2002, Authors 2005, and Paseau 2006), and the lesson of this debate seems to be that subtraction arguments, such as Baldwin’s and Schaffer’s, are faced with a dilemma: either they are invalid or they fail to be suasive. We outline how Baldwin’s argument can be reformulated so as to avoid both horns of this dilemma, and we then argue that Schaffer’s argument cannot so avoid the dilemma.