The core idea developed in this book is that phonological faithfulness requires preservation of underlying elements in surface forms. To formally implement this idea, I propose that input-output (10) faithfulness constraints are existentially quantified, such that they require each underlying element to have some faithful correspondent in the surface form. This is a departure from classic Correspondence Theory (McCarthy and Prince 1995), in which faithfulness constraints are universally quantified and require all output elements to be faithful to their input correspondent.