This paper demonstrates problems in allocating inter-station inventory capacities in unpaced production lines with heteroscedastic processing times. Simulations were performed to show the effects of total work-in-process inventory capacity, relative inter-station inventory allocations and pattern of processing time variances upon production rate, work station idle times and time to complete a product. Trade offs among the three performance measures were observed and deficiencies in intuitive strategies for redesigning lines were deduced.