Generalized regression is commonly used to adjust sampling weights to satisfy benchmark constraints. The resulting estimator of a total is design-consistent but some of the calibrated weights may not satisfy specified range restrictions. Several iterative modifications of generalized regression that attempt to meet both benchmark and range constraints have been proposed, but these methods may not yield a solution even if the range restrictions are mild, for example, restriction to nonnegative weights. A natural and practical way out of this difficulty is to make some of the benchmark constraints nonbinding up to specified tolerances while maintaining the other benchmark constraints as binding with zero tolerance.` The range restrictions themselves can be relaxed if necessary to get lower tolerance levels on benchmark constraints. For complex surveys, Chambers (1996) proposed a modification of the ridge regression method of Bardsley and Chambers (1984) that leads to a design-consistent estimator of a total in spite of the presence of a ridge (or inverse cost) matrix which makes the weights stable, although the benchmark constraints become nonbinding. We establish a relationship between the ridge matrix and the matrix of specified tolerances and then show that Chamber`s method can be adapted to meet benchmark constraints up to specified tolerances while maintaining design-consistency. This procedure is non iterative and easy to implement like the generalized regression, but it may not-meet -range restrictions despite relaxing of benchmark constraints. To address this problem, we propose an iterative method, termed ridge shrinkage, which generalizes the ridge regressions method in a manner similar to the iterative modifications of generalized regression, to meet range restrictions. This method is designed to force convergence for a specified number of iterations by using a built-in tolerance specification procedure; to relax benchmark constraints while satisfying range restrictions and maintaining design consistency. Empirical results on the performance of the proposed method are also presented.