Spatial interpolation methods used for estimation of missing precipitation data generally under and overestimate the high and low extremes, respectively. This is a major limitation that plagues all spatial interpolation methods as observations from different sites are used in local or global variants of these methods for estimation of missing data. This study proposes bias-correction methods similar to those used in climate change studies for correcting missing precipitation estimates provided by an optimal spatial interpolation method. The methods are applied to post-interpolation estimates using quantile mapping, a variant of equi-distant quantile matching and a new optimal single best estimator (SBE) scheme. The SBE is developed using a mixed-integer nonlinear programming formulation. K-fold cross validation of estimation and correction methods is carried out using 15 rain gauges in a temperate climatic region of the U.S. Exhaustive evaluation of bias-corrected estimates is carried out using several statistical, error, performance and skill score measures. The differences among the bias-correction methods, the effectiveness of the methods and their limitations are examined. The bias-correction method based on a variant of equi-distant quantile matching is recommended. Post-interpolation bias corrections have preserved the site-specific summary statistics with minor changes in the magnitudes of error and performance measures. The changes were found to be statistically insignificant based on parametric and nonparametric hypothesis tests. The correction methods provided improved skill scores with minimal changes in magnitudes of several extreme precipitation indices. The bias corrections of estimated data also brought site-specific serial autocorrelations at different lags and transition states (dry-to-dry, dry-to-wet, wet-to-wet and wet-to-dry) close to those from the observed series. Bias corrections of missing data estimates provide better serially complete precipitation time series useful for climate change and variability studies in comparison to uncorrected filled data series. Copyright © 2013 John Wiley & Sons, Ltd.