A well known sequential predictor-corrector regularization method for the stable solution of ill-posed Volterra problems is analysed. Under a certain stability assumption well-posedness and convergence results are obtained. Under the additional assumption of smoothness for the exact solution, convergence rates are proved. It is also proved that the stability condition cannot be satisfied for Volterra problems with ν-smoothing kernels, where ν≥5. Numerical examples are presented showing the stable and the unstable situations and verifying numerically the convergence rate result.