With our increasing reliance on cloud computing, accurate resource allocation of virtual machines (or domains) in the cloud have become more and more important. However, the current design of hypervisors (or virtual machine monitors) fails to accurately allocate resources to the domains in the virtualized environment. In this paper, we claim the root cause is that the protection scope is erroneously used as the resource scope for a domain in the current virtualization design. Such design flaw prevents the hypervisor from accurately accounting resource consumption of each domain. In this paper, using virtual CPUs as a container we propose to redefine the resource scope of a domain, so that the new resource scope is aligned with all the CPU consumption incurred by this domain. As a demonstration, we implement a novel system, called VASE (vCPU as a container), on top of the Xen hypervisor. Evaluations on our testbed have shown our proposed approach is effective in accounting system-wide CPU consumption incurred by domains, while introducing negligible overhead to the system.