Nanovesicles (similar to 100 nm) are ubiquitous in cell biology and an important vector for drug delivery. Mechanical properties of vesicles are known to influence cellular uptake, but the mechanism by which deformation dynamics affect internalization is poorly understood. This is partly due to the fact that experimental studies of the mechanics of such vesicles remain challenging, particularly at the nanometer scale where appropriate theoretical models have also been lacking. Here, we probe the mechanical properties of nanoscale liposomes using atomic force microscopy (AFM) indentation. The mechanical response of the nanovesicles shows initial linear behavior and subsequent flattening corresponding to inward tether formation. We derive a quantitative model, including the competing effects of internal pressure and membrane bending, that corresponds well to these experimental observations. Our results are consistent with a bending modulus of the lipid bilayer of similar to 1.4k(b)T. Surprisingly, we find that vesicle stiffness is pressure dominated for adherent vesicles under physiological conditions. Our experimental method and quantitative theory represents a robust approach to study the mechanics of nanoscale vesicles, which are abundant in biology, as well as being of interest for the rational design of liposomal vectors for drug delivery.