The Minimalist Program in generative syntax has been the subject of much rancour, a good proportion of it stoked by Noam Chomsky’s suggestion that language may represent “a ‘perfect solution’ to minimal design specifications.” A particular flash point has been the application of Minimalist principles to speculations about how language evolved in the human species. This paper argues that Minimalism is well supported as a plausible approach to language evolution. It is claimed that an assumption of minimal design specifications like that employed in MP syntax satisfies three key desiderata of evolutionary and general scientific plausibility: Physical Optimism, Rational Optimism, and Darwin’s Problem. In support of this claim, the methodologies employed in MP to maximise parsimony are characterised through an analysis of recent theories in Minimalist syntax, and those methodologies are defended with reference to practices and arguments from evolutionary biology and other natural sciences.