An effective procedure is presented that allows stable hole-drilling residual stress calculations using strain data from measurements taken at many small increments of hole depth. This use of many strain measurements is desirable because it improves the data content of the calculation, and the statistical reliability of the residual stress results. The use of Tikhonov regularization to reduce the noise sensitivity that is characteristic of a fine-increment calculation is described. This mathematical procedure is combined with the Morozov criterion to identify the optimal amount of regularization that balances the competing tendencies of noise reduction and stress solution distortion. A simple method is described to estimate the standard error in the strain measurements so that the optimal regularization can be chosen automatically. The possible use of a priori information about the trend of the expected solution is also discussed as a further means of improving the stress solution. The application of the described method is demonstrated with some experimental measurements, and realistic results are obtained.