In this paper we deal with the numerical solution of the Reissner-Mindlin plate problem with the use of high order finite elements. In previous papers we have solved the problem using approximation spaces of Serendipity type, in order to minimize the number of internal degrees of freedom. Since further numerical experiences have evidenced that the addition of bubble functions improved the quality of the results we have modified the previous family of hierarchic finite elements, adding internal degrees of freedom, to make a systematic analysis of their performance. Of course, more degrees of freedom are introduced. Nonetheless the numerical results indicate that the reduction of the error outnumbers the increase of degrees of freedom and therefore bubble plus elements are preferable.