The domain of positive Boolean functions, P os, is by now well established for the analysis of the variable dependencies that arise within logic programs. Analyses based on P os that use binary decision diagrams have been shown to be eecient for a wide range of practical programs. However, independent of the representation, assuming that P 6 = N P , an (unwidened) P os analysis can never come with any ee-ciency guarantees because of its potentially explosive behaviour. This paper proposes a simple widening for (goal-dependent) groundness analysis of logic programs that guarantees scalability and eeciency. Experimental results indicate that the widening induces only a very small loss of precision.