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In multi-product, multi-component periodic review assemble-to-order systems, the component allocation policy has substantial impact on performance. In this paper, the impact of two classes of non-first-come-first-served allocation rules (non-FCFS) are evaluated; i.e., the last-come-first-served-within-one-period, and the product-based-priority-within-time-windows approach. The demand fulfillment rates for these rules are expressed analytically, which are then used to formulate base stock level optimization problems as chance-constrained programs. Moreover, three mathematical programs are used as benchmarks to test the non-FCFS rules. They maximize both the average cycle service level and the aggregate fill-rate, and separately minimize the operational cost per period under the FCFS rule. We show that these simple non-FCFS rules can significantly improve service measures and often outperform the benchmarks, though operational costs increase moderately. Importantly, the value of these rules is greatest when the customer service is used as a point of differentiation. [ABSTRACT FROM AUTHOR]