We study the problem of revising specifications with preferences for automata based control synthesis problems. In this class of revision problems, the user provides a numerical ranking of the desirability of the subgoals in their specifications. When the specification cannot be satisfied on the system, then our algorithms automatically revise the specification so that the least desirable user goals are removed from the specification. We propose two different versions of the revision problem with preferences. In the first version, the algorithm returns an exact solution while in the second version the algorithm is an approximation algorithm with non-constant approximation ratio. Finally, we demonstrate the scalability of our algorithms and we experimentally study the approximation ratio of the approximation algorithm on random problem instances.