Ballistic Electron Emission Microscopy (BEEM) and finite-element electrostatic modeling were used to quantify how "small-size" effects modify the energy barrier at metal/semiconductor nanostructure nanocontacts, formed by making Schottky contacts to cleaved edges of GaAs quantum wells (QWs). The Schottky barrier height over the QWs was found to systematically increase with decreasing QW width, by up to ∼140 meV for a 1nm QW. This is mostly due to a large quantum-confinement increase (∼200 meV for a 1nm QW), modified by smaller decreases due to "environmental" electric field effects. Our modeling gives excellent quantitative agreement with measurements for a wide range of QW widths when both quantum confinement and environmental electric fields are considered.