A lot of sensor node platforms used for establishing wireless sensor networks (WSNs) can support multiple radio channels for wireless communication. Therefore, rather than using a radio single channel and sharing it for the whole network, multiple channels can be utilized in a sensor network simultaneously to decrease the overall interference in the network, which may help increasing the aggregate throughout in the network and decrease packet collisions and delay. This requires, however, appropriate channel assignment schemes to be used for assigning channels to the nodes for multi-channel communication in the network. Since, data generated by sensor nodes are usually carried to one or more sinks in the network using routing trees, tree-based channel assignment schemes are a natural approach for assigning channels in a WSN. We present two fast tree-based channel assignment schemes (called BUCA and NCCA) for multi-channel WSNs. We also propose a new network interference metric that is used in our algorithms while making decisions. We evaluate our proposed schemes by extensive simulation experiments and compare them with another well-known tree-based protocol from the literature. The results show that our proposed algorithms can provide better performance, up to 40% performance increase in some cases, compared to the other method. We also discuss in which cases the performance improvement can be achieved.