We report thorough experimental characterization of the nucleation and stationary propagation of self-healing slip pulses at a gel/glass interface under constant stress loading. We show that the slip front can be nucleated heterogeneously at the edges of the contact or homogeneously inside it. The resulting slip front can propagate both in the direction of slip or backwards; its velocity depends on the applied stress through a local tip process that is independent of specimen geometry. The backward tip velocity is slower than the front tip velocity by a factor of 4. Both velocities increase linearly with the applied stress jump, with a threshold below which no pulse can form. The pulse length and the total slip is found to be a linear function of the tip velocity. We address the complex problem of selection of the pulse velocity, length and associated slip by using a simplified analytical model. We emphasize the crucial role played by non-linearities of the friction law.