Tomographic ray tracing is the critical step in ray-based tomographic approaches when we need to represent as precisely as possible the wavepaths of the migration. To be able to update velocities from picked information in the migrated domain, one must be able to back propagate the misfocusing information (e.g., the residual moveout [RMO]) into the model through the tracing of tomographic rays. The complex kinematics associated with some types of migration, ray based or not, will give us RMO curvatures that will be impossible to explain with traditional tomographic ray-tracing methods. We have evaluated a generic method for tracing these rays by fitting constraints unique to each migration approach. We found that, on synthetic and real data, using the correct set of equations in the tomographic ray-tracing engine can make a significant difference in the velocity model update.