The Eilenberg Swindle is often used in the context of K-theory, to show that a K-theory spectrum is contractible, often to explain why it is necessary to restrict to finite (under some definition of finite) objects. Unfortunately, these arguments generally rely on an argument in K_0: showing that K_0 = 0, and then waving hands vigorously in order to demonstrate that of course the argument lifts to the entire spectrum. In this talk we discuss contexts in which such arguments work, and other contexts in which they do not. In particular, we will give two examples, one well-known and one novel, in which K_0 = 0 for Eilenberg Swindle-type arguments, but the K-theory spectrum is not contractible.