Considerable attention has been paid to safety trials that are intended to rule out specific levels of risk associated with products that are widely used, such as trials designed to put bounds on the level of cardiovascular risk due to drugs for patients with type 2 diabetes. Less well known are safety trials of products for rare diseases, where the difficulties encountered in large safety trials due to infrequent events are compounded by very small sample sizes and often by absence of a concurrent control group. In this talk, I will explore the problems unique to safety trials for rare diseases, and will focus on the specific example of safety trials for rare bleeding disorders such as Hemophilia A and B. I will describe how such trials are typically designed and analyzed, and will present some alternative approaches including group sequential, adaptive and Bayesian designs.