We provide an abstract approach to approximation with a wide range of regularity classes X in spaces of pseudocontinuable functions Kp Θ, where Θ is an inner function and p > 0. More precisely, we demonstrate a general principle, attributed to A. Aleksandrov, which asserts that if a certain linear manifold X is dense in Kq Θ for some q > 0, then X is in fact dense in Kp Θ for all p > 0. Moreover, for a rich class of Banach spaces of analytic functions X, we describe the precise mechanism that determines when X is dense in a certain space of pseudocontinuable functions. As a consequence, we obtain an extension of Aleksandrov's density theorem to the class of analytic functions with uniformly convergent Taylor series. © 2022 American Mathematical Society.