Open-pollinated (OP) mating is frequently used in forest tree breeding due to the relative temporal and financial efficiency of the approach. The trade-off is the lower precision of the estimated genetic parameters. Pedigree/sib-ship reconstruction has been proven as a tool to correct and complete pedigree information and to improve the precision of genetic parameter estimates. Our study analyzed an advanced generation Eucalyptus population from an OP breeding program using single-step genetic evaluation. The relationship matrix inferred from sib-ship reconstruction was used to rescale the marker-based relationship matrix (G matrix). This was compared with a second scenario that used rescaling based on the documented pedigree. The proposed single-step model performed better with respect to both model fit and the theoretical accuracy of breeding values. We found that the prediction accuracy was superior when using the pedigree information only when compared with using a combination of the pedigree and genomic information. This pattern appeared to be mainly a result of accumulated unrecognized relatedness over several breeding cycles, resulting in breeding values being shrunk toward the population mean. Using biased, pedigree-based breeding values as the base with which to correlate predicted GEBVs, resulted in the underestimation of prediction accuracies. Using breeding values estimated on the basis of sib-ship reconstruction resulted in increased prediction accuracies of the genotyped individuals. Therefore, selection of the correct base for estimation of prediction accuracy is critical. The beneficial impact of sib-ship reconstruction using G matrix rescaling was profound, especially in traits with inbreeding depression, such as stem diameter.