We study a coordination game where N players simultaneously and independently decide whether to take a certain action or not. Players’ payoffs depend only on how many players take each action (i.e., the coalition size) and there is incomplete information on players’ types: “Dominant” types have a dominant strategy and care about “enough” people taking an action. “Non-dominant” types do not have a dominant strategy due to non-monotone preferences over the coalition size: their payoffs are maximized when “enough” but “not too many” people take an action. We focus on the behavior of “non-dominant” types and show how the frequency of taking each action and (mis)coordination outcomes depend on the distribution of types and types’ preference heterogeneity. Our experimental results are (mostly) in line with our theoretical predictions: The frequency of coordination failure is not only increasing in the preference heterogeneity —as predicted by the theory, but is also increasing in the share of “non-dominant” types.