Contemporary management theories such as Just-in-Time and Total Quality Management emphasize variance reduction as a critical step in improving system performance. But little is said about how such efforts should be directed. Suppose a manager has only limited resources for variance reduction efforts. How should she allocate them among a set of competing activities? Which activity should receive highest priority? We explore such questions in the context of a synchronous assembly line where processing times are variable, incomplete jobs are reworked at the end of the line, and the objective is to minimize the total expected work overload. Our results indicate that the station with the highest variance may not always be the best choice for variance reduction. Identifying the set of stations that should receive variance reduction in an optimal solution is not trivial. Moreover, the variances at these stations may not be reduced by the same amount or to the same level. We establish that the remaining variables among stations that receive variance reduction must conform to one of two preferred structures: equal variance or spike-shaped. Dominance results are presented to identify the set of stations and the amount of reduction in an optimal solution.