Summary: I consider an ordered probit model in which some of the observations in one categories are missing. The model can be estimated because of a second variable with a similar truncation scheme. The second variable has the effect of increasing the number of categories quadratically while only increasing the number of parameters linearly. This model arises in the analysis of the effectiveness of helmets in reducing the severeity of head and neck injuries in motorcycle accidents. The problem is that accidents in which the rider did not receive a head or neck injury were observed only if the rider received a body injury, and vice versa. The results show that helmets are effective in reducing the severity of the worst head or neck injury but, because the worst overall injury that a rider receives is often a body injury, their effect of the severity of the worst overall injury is smaller.