In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in polynomial time. These characterizations are also extensionally complete -- they capture all functions -- but are not intensionally complete as some polytime algorithms are rejected. This impact on expressive power is an unavoidable cost of achieving a tractable characterization. To overcome this issue, an avenue arising from security applications is to find a relaxation of noninterference based on a declassification mechanism that allows critical data to be released in a safe and controlled manner. Following this path, we present a new and intuitive declassification policy preserving FP-soundness and capturing strictly more programs than existing noninterference-based systems. We show the versatility of the approach: it also provides a new characterization of the class BFF of second-order polynomial time computable functions in a second-order imperative language, with first-order procedure calls. Type inference is tractable: it can be done in polynomial time.