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Recently there has been increasing interest in systems which induce rst order logic programs from examples. However, many di culties need to be overcome. Well-known algorithms fail to discover correct logical descriptions for large classes of interesting predicates, due either to the intractability of search or overly strong limitations applied to the hypothesis space. In contrast, search is avoided within Plotkin's framework of relative least general generalisation (rlgg). It is replaced by the process of constructing a unique clause which covers a set of examples relative to given background knowledge. However, such a clause can in the worst case contain in nitely many literals, or at best grow exponentially with the number of examples involved. In this paper we introduce the concept of h-easy rlgg clauses and show that they have nite length. We also prove that the length of a certain class of\determinate" rlgg is bounded by a polynomial function of certain features of the background knowledge. This function is independent of the number of examples used to construct them. An existing implementation called GOLEM is shown to be capable of inducing many interesting logic programs which have not been demonstrated to be learnable using other algorithms.