While providing anonymity at terminal devices (e.g. Android and iOS devices) is beneficial for users (e.g. consuming services and resources without the risk of being traced), relevant stakeholders (e.g. providers and governments) may require conditional anonymity for billing purpose or to locate dishonest or compromised client devices. In a cloud computing deployment where large number of computation tasks are submitted to the public cloud, the public cloud server may encounter computation peak and hence, responses to the terminal devices may be delayed. Thus, in this paper, we design the first precise reward scheme achieving both anonymity and traceability for crowdcomputing in public clouds. We then prove the security of the proposed scheme in the random oracle model, and demonstrate the practicality of the scheme using simulations.