Magnetic tunnel junctions with perpendicular magnetic anisotropy are investigated using a conductive atomic force microscope. The 1.23 nm Co40Fe40B20 recording layer coercivity exhibits a size dependence which suggests single domain behavior for diameters ≤ 100 nm. Focusing on devices with diameters smaller than 100 nm, we determine the effect of voltage and size on the effective device anisotropy Keff using two different techniques. Keff is extracted both from distributions of the switching fields of the recording and reference layers, and from measurement of thermal fluctuations of the recording layer magnetization when a field close to the switching field is applied. The results from both sets of measurements reveal that Keff increases monotonically with decreasing junction diameter, consistent with the size dependence of the demagnetization energy density. We demonstrate that Keff can be controlled with a voltage down to the smallest size measured, 64 nm. PACS numbers: 85.75.-d,73.40.Gk,75.78.-n,75.70.-i