It is commonly assumed that all propositions have modal profiles and therefore bear their truth-values either contingently or necessarily. I argue against this commonly assumed view and in defence of amodalism, according to which certain true propositions are neither necessarily nor contingently true, but only true simpliciter. I consider three arguments against ‘possible-worlds theories’, which hold that modal concepts are to be analysed in terms of possible worlds. Although each of these arguments targets a different version of possible-worlds theory, these versions jointly exhaust the entire range of possible-worlds theories. After showing that each argument is naturally addressed by adopting amodalism, I argue that all defenders of possible-worlds theory ought to accept amodalism.