Background: Recent advances in the development of enzyme cocktails for degradation of lignocellulosic biomass, especially the discovery of lytic polysaccharide monooxygenases (LPMOs), have opened new perspectives for process design and optimization. Softwood biomass is an abundant resource in many parts of the world, including Scandinavia, but efficient pretreatment and subsequent enzymatic hydrolysis of softwoods are challenging. Sulfite pulping-based pretreatments, such as in the BALI™ process, yield substrates that are relatively easy to degrade. We have assessed how process conditions affect the efficiency of modern cellulase preparations in processing of such substrates. Results: We show that efficient degradation of sulfite-pulped softwoods with modern, LPMO-containing cellulase preparations requires the use of conditions that promote LPMO activity, notably the presence of molecular oxygen and sufficient reducing power. Under LPMO activity-promoting conditions, glucan conversion after 48-h incubation with Cellic® CTec3 reached 73.7 and 84.3% for Norway spruce and loblolly pine, respectively, at an enzyme loading of 8 mg/g of glucan. The presence of free sulfite ions had a negative effect on hydrolysis efficiency. Lignosulfonates, produced from lignin during sulfite pretreatment, showed a potential to activate LPMOs. Spiking of Celluclast®, a cellulase cocktail with low LPMO activity, with monocomponent cellulases or an LPMO showed that the addition of the LPMO was clearly more beneficial than the addition of any classical cellulase. Addition of the LPMO in reactions with spruce increased the saccharification yield from approximately 60% to the levels obtained with Cellic® CTec3. Conclusions: In this study, we have demonstrated the importance of LPMOs for efficient enzymatic degradation of sulfite-pulped softwood. We have also shown that to exploit the full potential of LPMO-rich cellulase preparations, conditions promoting LPMO activity, in particular the presence of oxygen and reducing equivalents are necessary, as is removal of residual sulfite from the pretreatment step. The use of lignosulfonates as reductants may reduce the costs related to the addition of small molecule reductants in sulfite pretreatment-based biorefineries.