This article presents a new computational model for the generation of multimodal referring expressions (REs), based on observations in human communication. The algorithm is an extension of the graph-based algorithm proposed by Krahmer, van Erk, and Verleg (2003) and makes use of a so-called Flashlight Model for pointing. The Flashlight Model accounts for various types of pointing gestures of different precisions. Based on a notion of effort, the algorithm produces REs combining language and pointing gestures. The algorithm is evaluated using two production experiments with which spontaneous data is gathered on controlled input. The output of the algorithm coincides to a large extent with the utterances of the participants. However, an important difference is that the participants tend to produce overspecified REs, whereas the algorithm generates minimal ones. This article briefly discusses ways to generate overspecified multimodal references. (Contains 11 figures, 5 tables and 7 footnotes.)