In task-oriented communication, references often need to be effective in their distinctive function, that is, help the hearer identify the referent correctly and as effortlessly as possible. However, it can be challenging for computational or empirical studies to capture referential effectiveness. Empirical findings indicate that human-produced references are not always optimally effective, and that their effectiveness may depend on different aspects of the situational context that can evolve dynamically over the course of an interaction. On this basis, we propose a computational model of effective reference generation which distinguishes speaker behaviour according to its helpfulness to the hearer in a certain situation, and explicitly aims at modelling highly helpful speaker behaviour rather than speaker behaviour invariably. Our model, which extends the planning-based paradigm of sentence generation with a statistical account of effectiveness, can adapt to the situational context by making this distinction newly for each new reference. We find that the generated references resemble those of effective human speakers more closely than references of baseline models, and that they are resolved correctly more often than those of other models participating in a shared-task evaluation with human hearers. Finally, we argue that the model could serve as a methodological framework for computational and empirical research on referential effectiveness.