Certain embodiments of the surgical instruments provided according to the invention utilize a channel positioned adjacent to and downstream of a liquid jet-forming nozzle such that at least a portion of the liquid jet passes at least one of within the channel and adjacent to and along the length of at least a portion of a longitudinally-oriented opening in the channel, when the instrument is in operation. The use of such channels in certain embodiments of the inventive surgical instruments can enable the instruments to provide enhanced control over the depth and degree of cutting and/or ablation of tissue; and/or can provide improved and enhanced functionality for cleaning, debriding, and/or trimming and cutting a tissue/surface; and/or can provide longer effective liquid jet beam cutting/ablation lengths by reducing the degree of dispersion of the jet along its length.