Water is the most common liquid on this planet, with many unique properties that make it essential for life as we know it. These properties must arise from features in the charge distribution of a water molecule, so it is essential to capture these features in potential energy functions for water to reproduce its liquid state properties in computer simulations. Recently, models that utilize a multipole expansion located on a single site in the water molecule, or "molecular multipole models", have been shown to rival and even surpass site models with up to five sites in reproducing both the electrostatic potential around a molecule and a variety of liquid state properties in simulations. However, despite decades of work using multipoles, confusion still remains about how to truncate the multipole expansions efficiently and accurately. This is particularly important when using molecular multipole expansions to describe water molecules in the liquid state, where the short-range interactions must be accurate, because the higher order multipoles of a water molecule are large. Here, truncation schemes designed for a recent efficient algorithm for multipoles in molecular dynamics simulations are assessed for how well they reproduce results for a simple three-site model of water when the multipole moments and Lennard-Jones parameters of that model are used. In addition, the multipole analysis indicates that site models that do not account for out-of-plane electron denSity overestimate the stability of a non-hydrogen-bonded conformation, leading to serious consequences for the simulated liquid.