Sodium dodecyl sulfate (SDS) is a well-known protein denaturing agent. A less known property of this detergent is that it can activate or inactivate some enzymes at sub-denaturing concentrations. In this work we explore the effect of SDS on the ATPase activity of a hyper-thermophilic and a mesophilic Cu(I) ATPases reconstituted in mixed micelles of phospholipids and a non-denaturing detergent. An iterative procedure was used to evaluate the partition of SDS between the aqueous and the micellar phases, allowing to determine the composition of micelles prepared from phospholipid/detergent mixtures. The incubation of enzymes with SDS in the presence of different amounts of phospholipids reveals that higher SDS concentrations are required to obtain the same degree of inactivation when the initial concentration of phospholipids is increased. Remarkably, we found that, if represented as a function of the mole fraction of SDS in the micelle, the degree of inactivation obtained at different amounts of amphiphiles converges to a single inactivation curve. To interpret this result, we propose a simple model involving active and inactive enzyme molecules in equilibrium. This model allowed us to estimate the Gibbs free energy change for the inactivation process and its derivative with respect to the mole fraction of SDS in the micellar phase, the latter being a measure of the susceptibility of the enzyme to SDS. Our results showed that the inactivation free energy changes are similar for both proteins. Conversely, susceptibility to SDS is significantly lower for the hyperthermophilic ATPase, suggesting an inverse relation between thermophilicity and susceptibility to SDS.