While the services-based model of cloud computing makes more and more IT resources available to a wider range of customers, the massive amount of data in cloud platforms is becoming a target for malicious users. Previous studies show that attackers can co-locate their virtual machines (VMs) with target VMs on the same server, and obtain sensitive information from the victims using side channels. This paper investigates VM allocation policies and practical countermeasures against this novel kind of co-resident attack by developing a set of security metrics and a quantitative model. A security analysis of three VM allocation policies commonly used in existing cloud computing platforms reveals that the server's configuration, oversubscription and background traffic have a large impact on the ability to prevent attackers from co-locating with the targets. If the servers are properly configured, and oversubscription is enabled, the best policy is to allocate new VMs to the server with the most VMs. Based on these results, a new strategy is introduced that effectively decreases the probability of attackers achieving co-residence. The proposed solution only requires minor changes to current allocation policies, and hence can be easily integrated into existing cloud platforms to mitigate the threat of co-resident attacks.