We focus on architectures with limited flexibility for multi-skill call centers. The context is that of call centers with asymmetric parameters: unbalanced workload, different service requirements, a predominant customer type, unbalanced abandonments and high costs of cross-training. The most well-known architectures with limited flexibility such as chaining fail against such asymmetry. We propose a new architecture referred to as single pooling with only two skills per agent and we demonstrate its efficiency. Using simulation, we conduct a comprehensive comparison between this architecture and chaining. As a function of the various system parameters, we delimit the regions where either chaining or single pooling is the best. Single pooling leads to a better performance than chaining while being less costly under various situations of asymmetry: asymmetry in the number of arrivals, in the service durations, in the variability of service times, or in the service level requirements. It is also shown that these observations are more apparent for situations with a large number of skills, or for those with a large call center size. &