When do children extend a construction (“rule”) productively? A recent Threshold proposal claims that a construction is productive if and only if it has been witnessed applying to a sufficient proportion of cases and sufficiently few exceptions. An alternative proposal, Communicate + Access (C&A), argues that children extend a construction productively because they wish to express an intended message and are unable to access a “better” (appropriate and more conventional) way to do it. Accessibility, in turn, is negatively affected by interference from competing alternatives. In a (preregistered) experiment, 32 4-6-year-old children were provided with exposure to 2 mini-artificial languages for which the two proposals make opposite predictions. Results support the C&A proposal: children were more productive after witnessing 3 rule-following cases than after 5, due to differences in interference. We conclude that productivity is encouraged by a desire to communicate a message and is constrained by accessibility/interference.