We consider bargaining problems with at least one cardinal player and with ordinal players, and provide a complete description of utility invariant solutions of such problems for two players. For the n-person case we provide a procedure that: (i) returns a given cardinal solution if there are only cardinal players; (ii) is based on the ordinal solution for gradual bargaining problems, introduced by o'neill et al. [o'neill, b., samet, d., wiener, z., winter, e., 2002. Bargaining with an agenda. Games econ. Behav., in press], for the ordinal players. Finally, we introduce the so-called cardinal concession solution as another example of a utility invariant solution.