We compare several statistical routines that may be used to calculate d 18 O sw and SSS from paired coral Sr/Ca and d 18 O measurements. Typically, the d 18 O coral -SST relationship is estimated by linear regression of coral d 18 O vs. SST. If this method is applied, evidence should be given that at a particular site SST and SSS do not co-vary. In the tropical oceans, SST and d 18 O sw (SSS) often co-vary, and this will bias the estimate of the regression slope of d 18 O coral -SST. Using a stochastic model, we show that covariance leads to a bias in the coefficients of the univariate regression equations. As the slope of the d 18 O coral -SST relationship has known, we propose to insert this value for c 1 in the regression models. This requires that the constants of the regression equations are removed. To omit the constants, we propose to center the regression equations (i.e., to remove the mean values from the variables). The statistical error propagation is calculated to assess our ability to resolve past variations in d 18 O sw (SSS). At Tahiti, we find that the combined analytical uncertainties of coral d 18 O and Sr/Ca equal the amplitude of the seasonal cycle of d 18 O sw (SSS). Therefore, we cannot resolve the seasonal cycle of SSS at Tahiti. At Timor, the error of reconstructed d 18 O sw (SSS) is lower than the magnitude of seasonal variations of d 18 O sw (SSS), and the seasonal cycle of d 18 O sw (SSS) can be resolved.