This paper addresses multi-resource fair allocation: a fundamental research topic in cloud computing. To improve resource utili-zation under well-studied faess constraints, we propose a new allocation mechanism called Dominant Resource with Bottlenecked Faess (DRBF), which generalizes Bottle-neck-aware Allocation (BAA) to the settings of Dominant Resource Faess (DRF). We classify users into different queues by their dominant resources. The goals are to ensure that users in the same queue receive alloca-tions in proportion to their fair shares while users in different queues receive allocations that maximize resource utilization subject to well-studied faess properties such as those in DRF. Under DRBF, no user 1) is worse off sharing resources than dividing resources equally among all users; 2) prefers the alloca-tion of another user; 3) can improve their own allocation without reducing other users’ alloca-tions; and (4) can benefit by misreporting their resource demands. Experiments demonstrate that the proposed allocation policy performs better in terms of high resource utilization than does DRF.