The need to reduce power and complexity will increase the interest in Switch on Event multithreading (coarse grained multithreading). Switch On Event multithreading is a low power and low complexity mechanism to improve processor throughput by switching threads on execution stalls. Fairness may, however, become a problem in a mul- tithreaded processor. Unless fairness is properly handled, some threads may starve while others consume all of the processor cycles. Heuristics that were devised in order to improve fairness in Simultaneous Multithreading are not applicable to Switch On Event multithreading. This paper defines the fairness metric using the ratio of the individ- ual threads? speedups, and shows how it can be enforced in Switch On Event multithreading. Fairness is controlled by forcing additional thread switch points. These switch points are determined dynamically by runtime estimation of the single threaded performance of each of the individ- ual threads. We analyze the impact of the fairness enforce- ment mechanism on throughput. We present simulation re- sults of the performance of Switch on Event multithread- ing. Switch on Event multithreading achieves an average speedup over single thread of 24% when no fairness is en- forced. In this case, over a third of our runs achieved poor fairness in which one thread ran extremely slowly (10 to 100 times slower than its single thread performance) while the other thread?s performance was hardly affected. By using the proposed mechanism we can guarantee fairness of 1/4, 1/2 and 1 for a small performance loss of 2.2%, 3.7% and 7.2% respectively.