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Prosopis alba is a native forest tree growing in arid and semi-arid regions of Argentina. It is a multipurpose species suitable for silvopastoral systems. The breeding programmes of P. alba in Argentina started similar to 25 years ago. Although several important advances have been made, the number of experimental stands is small in comparison with other forest species. In this study genetic parameters in several traits of economic importance were evaluated, including tree form (number of stems), height, diameter and size increments in an experimental stand. These traits exhibit significant heritabilities. The trade-off between genetic gain and increase of average kinship in the selected group was considered. With an elite group of 20 trees, the average group kinship drops from 0.5 to 0.03. An important constraint to selecting multiple traits was that the improvement on height and diameter was associated with a reduction in the form of the trees. The strategy of using a selection index was evaluated giving variable weights to tree form, height and diameter. Although gain at individual trait levels is reduced in comparison with the potential maximum, index selection allows significant gains for all three traits and represents a suitable strategy to improve P. alba stands in order to establish clonal seed orchards.