The objective of this paper was to (i) estimate genetic parameters for important physic nut (Jatropha curcas L.) traits, and to using these parameters (ii) predict the genetics gains with the selection of superior genotypes using different selection procedures. It was among the objectives of this paper to (iii) compare the efficiency of the different selection methods in order to identify the most suited to be applied in the physic nut breeding program. Broad sense heritabilities in the level of families were elevated (superior to 60% for yield for example) indicating that there are good prospects for the selection of superior genotypes. Combined selection (CS) provided the highest genetic gain (99.3%), followed by the stratified mass selection (SMS), selection among and within families (SAWF) and mass selection (MS). The number of selected families followed the inverse order indicating that the methods that generate the highest gains may deplete the genetic variability of the breeding population faster than the methods that provide intermediate gains. Considering, however, that the demand for improved physic nut cultivars is increasing each year in Brazil and considering that physic nut genetic basis in Brazil is already considered to be low, the addition of more diversity to breeding population will be needed, regardless of the selection procedure employed. Therefore, on the basis of the predicted genetic gains, CS seems to be more suited than other methods for rapid improvement of the species. Based on this strategy, genotypes with enhanced productivity, may be successfully selected in the Brazilian physic nut population and tested in expanded trials to be released as improved physic nut cultivars.