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Networks-on-Chip (NoCs) are a promising interconnect paradigm to address the communication bottleneck of Systems-on-Chip (SoCs). Wormhole flow control is widely used as the transmission protocol in NoCs, as it offers high throughput and low latency. To match the application characteristics, customized irregular topologies and routing functions are used. With wormhole flow control and custom irregular NoC topologies, deadlocks can occur during system operation. Ensuring a deadlock free operation of custom NoCs is a major challenge. In this paper, we address this important issue and present a method to remove deadlocks in application-specific NoCs. Our method can be applied to any NoC topology and routing function, and the potential deadlocks are removed by adding minimal number of virtual or physical channels. Experiments on a variety of realistic benchmarks show that our method results in a large reduction in the number of resources needed (88% on average) and NoC power consumption, area reduction (66% area savings on average) when compared to the state-of-the-art deadlock removal methods.