Encapsulation of molecules in phospholipid vesicles provides unique opportunities to study chemical reactions in small volumes as well as the behavior of individual proteins, enzymes, and ribozymes in a confined region without requiring a tether to immobilize the molecule to a surface. These experiments generally depend on generating a predictable loading of vesicles with small numbers of target molecules and thus raise a significant measurement challenge, namely, to quantify molecular occupancy of vesicles at the single-molecule level. In this work, we describe an imaging experiment to measure the time-dependent fluorescence from individual dye molecules encapsulated in similar to 130 nm vesicles that are adhered to a glass surface. For determining a fit of the molecular occupancy data to a Poisson model, it is critical to count empty vesicles in the population since these dominate the sample when the mean occupancy is small, lambda <= similar to 1. Counting empty vesicles was accomplished by subsequently labeling all the vesicles with a lipophilic dye and reimaging the sample. By counting both the empty vesicles and those containing fluors, and quantifying the number of fluors present, we demonstrate a self-consistent Poisson distribution of molecular occupancy for well-solvated molecules, as well as anomalies due to aggregation of dye, which can arise even at very low solution concentrations. By observation of many vesicles in parallel in an image, this approach provides quantitative information about the distribution of molecular occupancy in a population of vesicles.