A BOUNDED LINEAR OPERATOR T ON A HILBERT SPACE H ISN-SUPERCYCLIC, IF THERE IS A SUBSPACE E OF DIMENSION N SUCH THATITS ORBIT UNDER T IS DENSE IN H. ALSO, T IS AN (M, P) -ISOMETRY IF "FORMULA" AND M ³ 1. WE SHOW THAT THE SUM OF AN (M, P) -ISOMETRY ANDA NILPOTENT OPERATOR THAT COMMUTE WITH EACH OTHER IS NOT NSUPERCYCLIC FOR ANY POSITIVE INTEGER N, AND EVERY RATIONAL NUMBER P.