A novel hybrid switching technique for computer networks is proposed and analysed in this paper. This hybrid switching technique combines packet switching and cut-through switching. Partial cuts are introduced to improve the performance of a network from a practical point of view. Messages are segmented into packets using a threshold-based segmentation rule. A method to calculate reassembly delay for noisy channels is described and has been used in the analysis of the hybrid switching. Several numerical results are reported at the end which depict the practical versatility of the proposed hybrid switching. Some simulation results are also reported in order to verify the analytical formulation.