Optimistic systems execute events out of order and must undo their errors to produce correct results. Undoing incorrect work can be expensive. By restraining their optimism, such systems might execute fewer events out of order and thereby run faster. This paper examines two methods tested in the Time Warp Operating System. The first method explicitly prevents events from executing in the far simulation future. The second method tries to identify objects that are doing work that has to be undone; such objects are allowed to execute less often. Experimental results show that only modest gains were realized, and that even these gains were unpredictable. While other methods remain untested, the value of limiting optimism seems small.