Over the past decade, it has become clear that TNO and asteroid binary orbits cannot be modeled with simple Keplerian orbits. The aspherical nature of many of these bodies instead requires the use of a more complicated orbital model, one which approximates the potential of an aspherical body by adding gravitational potential harmonics. The majority of studies that include a harmonic expansion only use zonal harmonic terms (J2, J4, …), the terms that describe the oblateness of a body, and ignore sectoral terms (C22, C42, C44, …), those that describe the prolateness of a body. This implicitly assumes that any prolateness present will “average out”. In this presentation we question this assumption. We will show that, in a surprisingly wide variety of circumstances, sectoral terms can introduce significant changes to the non-Keplerian effects produced in orbits around triaxial primaries. We apply our results to a variety of systems and show that including these effects produces more accurate results.