Pure, or type-free, linear lambda calculus is Turing complete once reduction is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing reduction to be problematic from a complexity point of view. Modal impredicativity occurs when, during reduction, a residual of a box b interacts with the body of another residual of b. Technically speaking, superlazy reduction is a new notion of reduction that allows to control modal impredicativity. More specifically, superlazy reduction replicates a box only when all its copies are opened. This makes the overall cost of reducing a (linear) lambda-term finite and predictable. Specifically, superlazy reduction applied to any pure proof nets takes primitive recursive time. Moreover, any primitive recursive function can be computed by a lambda-term via superlazy reduction.