We study a class of non-protected local composite operators which occur in the R-symmetry singlet channel of the OPE of two stress-tensor multiplets in SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N² with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states.