No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing the experimental nuclear spectra. While a great deal of work has been directed toward computing effective interactions from bare nucleon-nucleon (NN) and three-nucleon forces, less progress has been made in calculating the effective operators. Thus, except for the relative kinetic energy, the proton radius, and the NN pair density, all investigations have used bare operators. We apply the Lee-Suzuki procedure to general two-body operators, investigating the importance of the approximations involved. In particular we concentrate on the limitations of the two-body cluster approximation.