Researchers designing choice modelling experiments have some latitude over the number of choice alternatives that can be offered in each choice set. There is some evidence that design dimensions, including the number of alternatives available in each choice set, can influence model outcomes. A key issue is whether referendum formats with binary options are preferable to choice sets with multiple alternatives. A choice modelling experiment was performed where questionnaires delivered to two split samples differed only according to whether two or three alternatives were offered to respondents in each choice set. The results indicate that more robust models could be constructed from the three-alternative split compared to the two-alternative split. One reason for the difference is that respondents tended to display serial non-participation in the two-alternative format, choosing an alternative consistently without regard for changes in the attributes. For practitioners of the CM technique, the results suggest that it may be preferable to offer more than two alternatives in a choice set that includes a status quo option.