All cellular functions involving deformation of the plasma membrane (e.g. endocytosis, exocytosis, the formation of surface protrusions) are regulated by the apparent membrane tension (Tm), a composite of the surface tension (σ) and the adhesion provided by molecules linking membrane to the actin cytoskeleton (γ). Using an optical trap based tether force assay, we recently demonstrated that class I myosins, a family of membrane-binding actin-based motor proteins, control membrane tension by mediating membrane-cytoskeleton adhesion. More specifically, these studies revealed that the membrane-cytoskeleton adhesion provided by myosin-I increases apparent membrane tension as indicated by the force required to pull a single membrane tether from the cell surface. Interestingly, the physical links to the cytoskeleton provided by myosin-I also allow the cell to form multiple adjacent tethers. However, when multiple tethers are pulled, tether lifetimes appear to decrease as apparent membrane tension increases. Here we present a thermodynamic model, which accounts for the impact of apparent membrane tension on the lifetime of multiple tethers. We argue that, in the context of our experimental geometry, the global increase in apparent membrane tension that results from greater membrane-cytoskeleton adhesion, works locally to accelerate the rupture of bonds between the membrane and cytoskeleton, which would otherwise prevent individual membrane tethers from coalescing. We also elaborate on this concept to develop a separate model, which shows that tuning the level of membrane-cytoskeleton adhesion may enable cells to vary the density of surface protrusions (i.e. # of structures per unit area membrane). As such, myosin-I dependent membrane-cytoskeleton adhesion emerges as the key regulator of cell surface morphology.