Lignocellulosic biomass is a sustainable industrial substrate. Copper-dependent lytic polysaccharidemonooxygenases (LPMOs) contribute to the degradation of lignocellulose and increase the efficiency of biofuel production. LPMOs can contain non-catalytic carbohydrate binding modules (CBMs), but their role in the activity of these enzymes is poorly understood. Here we explored the importance of CBMs in LPMO function. The family 2a CBMs of two monooxygenases, CfLPMO10 and TbLPMO10 from Cellulomonas fimi and Thermobispora bispora, respectively, were deleted and/or replaced with CBMs from other proteins. The data showed that the CBMs could potentiate and, surprisingly, inhibit LPMO activity, and that these effects were both enzyme-specific and substrate-specific. Removing the natural CBM or introducing CtCBM3a, from the Clostridium thermocellum cellulosome scaffoldin CipA, almost abolished the catalytic activity of the LPMOs against the cellulosic substrates. The deleterious effect of CBM removal likely reflects the importance of prolonged presentation of the enzyme on the surface of the substrate for efficient catalytic activity, as only LPMOs appended to CBMs bound tightly to cellulose. The negative impact of CtCBM3a is in sharp contrast with the capacity of this binding module to potentiate the activity of a range of glycoside hydrolases including cellulases. The deletion of the endogenous CBM from CfLPMO10 or the introduction of a family 10 CBM from Cellvibrio japonicus LPMO10B into TbLPMO10 influenced the quantity of non-oxidized products generated, demonstrating that CBMs can modulate the mode of action of LPMOs. This study demonstrates that engineered LPMO-CBM hybrids can display enhanced industrially relevant oxygenations.