An iterated version of the Lavrentiev's method, in the setting of a Banach space, is suggested for obtaining stable approximate solutions for the ill-posed operator equation Au = v, when the data A and v are known only approximately. In the setting of a Hilbert space with appropriate a priori parameter choice, the suggested procedure yields order optimal error estimates. An iterated version of Tikhonov regularization yielding order optimal error estimate is a special case of the procedure. The assumption on the approximating operators show that the finite dimensional system arising out of it would be of smaller size for larger iterates. This aspect is compared with an assumption of [3] for a degenerate kernel method for integral equations of the first kind. © 2000, by Walter de Gruyter GmbH & Co. All rights reserved.