Medical malpractice insurance is considered a unprofitable market in many countries, and this is why many policies have been implemented to increase its attractiveness for private insurers. We test the effects of limits to noneconomic compensations- scheduled damages- using Italian data. We estimate the average treated effect of schedules and whether it depends on the judicial efficiency, measured as court backlog. Our identification rests on the partial overlap between healthcare authorities districts and judicial districts, thus the caseload of a court and malpractice events at the healthcare provider level are not perfectly correlated. On average, the adoption of schedules does not produce any significant effect on insurers and paid premiums. However, it has a robust and significant effect on the number of insurers only in inefficient courts. We further investigate these findings using data for 17,578 malpractice insurance claims. We find evidence of a composition effect among claims which is triggered by higher levels of judicial inefficiency: the more inefficient a court, the lower the probability to have a case not decided on the merits, and the higher the level of reserve and recovery per claim. These results shed light on previous conflicting evidence in the literature.