In this paper we present a feed forward controller to regulate the depth of laser incisions in soft tissue. Such a controller is compatible with the requirements of laser microsurgery, where space constraints limit the use of sensing devices. The controller is based on an inverse model that maps the desired incision depth to the required laser exposure time. This model is extracted from experimental data through the use of statistical learning methods. To prove the concept, the controller is implemented in a robot-assisted laser microsurgery system that enables precision control of exposure time and laser motion. The validity and the accuracy of the controller is verified experimentally on ex-vivo muscle tissue (chicken breast), revealing an RMSE of 0.12 mm for incisions ranging up to 1 mm. In addition, we demonstrate how the model can be used to implement the automatic ablation of entire volumes of tissue, through the superposition of controlled laser incisions.