Hybrid switching combines a high-bandwidth optical circuit switch in parallel with a low-bandwidth electronic packet switch. It presents an appealing solution for scaling datacenter architectures. Unfortunately, it does not fut many trafic patterns produced by typical datacenter applications, and in particular the skewed trafic patterns that involve highly intensive one-tomany and many-to-one communications. In this paper, we introduce composite-path switch- ing by allowing for composite circuit/packet paths between the two switches. We show how this enables the datacenter network to deal with skewed trafic pat- terns, and offer a practical scheduling algorithm that can directly extend anyhybrid-switching scheduling algorithm. Through extensive evaluations using modern datacenter workloads, we show how our solution outperforms two recently proposed state-of-the-art scheduling techniques, both in completion time and in circuit uti- lization.