Accurate characterization of exoplanet orbits requires multiple observations made over one or more orbital periods. We use a rejection sampling algorithm to study how uncertainty in the observation data manifests in the computed orbital parameters and how this uncertainty depends on the number and spacing of observations. We find that 3 observations equally spaced over at least one half of an orbital period robustly reduces the uncertainty in the semi-major axis and eccentricity to below 10%. We also study modifications of this revisit strategy in the presence of a central obscuration and show how null observations may still be leveraged to constrain a detected exoplanets orbital parameters. Finally, we suggest a method for incorporating photometric data into the rejection sampling framework to break degeneracy in the orbit fitting procedure and further constrain the orbital parameters.