eduction strategies for logic programs often use an abstraction operator to guarantee the niteness of the set of goals for which partial deductions are . Findingan abstraction operator which guarantees niteness and does not lose relevant informationis a di cultproblem. In earlier work Gallagherand he proposed to base the abstraction operator on characteristic paths and trees, which capture the structure of the generated incomplete SLDNF-tree for a given goal. In this paper we exhibit the advantages of characteristic trees over purely syntactical measures: if characteristic trees can be preserved upon generalithen we obtain an almost perfect abstraction operator, providing just enough polyvariance to avoid any loss of local specialisation. Unfortunately, the abstraction operators proposed in earlier work do not always preserve the characteristic trees upon generalisation. We show that this can lead to important specialisation losses as well as to non-termination of the partial deductio...