The authors study a class of discrete predictor-corrector methods for the sequential regularization of first-kind Volterra integral equations. The method preserves the Volterra structure of the original problem and requires \(O(N^2)\) arithmetic operations, whereas the standard Tikhonov regularization is of computational complexity \(O(N^3)\). The authors establish a convergence theory for this method and present numerical examples, illustrating the adaptive selection of regularization parameters.