A totally chlorine free (TCF) bleaching sequence was studied for an acid sulfite pulp mill that produces dissolving pulps. Laboratory analyses of the last two bleaching stages, an oxidant-reinforced alkaline extraction stage (EOP), and a subsequent pressurized peroxide with oxygen stage (PO), were performed on a eucalypt pulp that had been delignified by an ozone (Z) stage in the pulp mill. The goal was to predict the optimal costs and operational conditions for the (EOP)(PO) partial bleach sequence for three different specialty pulp products. Four independent variables affecting the pulp quality properties were examined for each stage (i.e., reaction temperature, reaction time, NaOH dosage and H2O2 dosage). The dependent variables were various pulp properties, such as intrinsic pulp viscosity, alpha-cellulose content, kappa number, and GE brightness. Three scenarios were considered to optimize the bleaching process, which related to a regenerated cellulose product (viscose) that is widely commercialized, and to two novel products (nanocrystalline cellulose (NCC) and nanofibrillated cellulose (NFC). Statistical response surface models indicated that the bleaching behavior of the ozone-treated pulp could be represented by second-order polynomial equations. These non-linear optimization models predict cost savings of 62.2%, 73.4%, and 63.3% for producing viscose, NCC, and NFC pulp grades, respectively.