Abstract: Polling models are multiple queue, cyclic service systems which are served by one server. In our case, the feature of the server is that it may be forced to wait idly for new jobs at an empty queue instead of switching to the next station. We propose different wait-and-see strategies that govern these waiting periods. We assume Poisson arrivals for new jobs and allow general service and switchover time distributions. A performance measure of interest is the mean average queueing delay. The results are formulas for this delay and characterisations of the cases where the wait-and-see strategies yield a lower delay compared to the exhaustive strategy.