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tokens: used the local Maxwellian approximation to generate their ICs, which can lead to artificial relaxation in the centre of the subhalo (Kazantzidis et al. 2004 ). Overall, it appears that the fits from Green van den Bosch ( 2019 ) perform slightly better than all other models, but our model is at least comparable to, if not more accurate than the models presented in Hayashi et al. ( 2003 ) and Peñarrubia et al. ( 2010 ). Figure 1. Comparison of different model descriptions of the density, enclosed mass, and circular velocity profiles of the bound satellite remnant after one orbit in the Slow (left-hand panel) and Fast Simulation (right-hand panel). Simulation results are shown with points, and the models are shown with lines. The thick dashed curve shows the original, untruncated NFW profile. The residuals in the fits are calculated as ( y model / y simulation − 1), where y is the density, mass, or circular velocity profile. Our model from Paper I is described in Section 2 , and the other models in Appendix B . In all cases, the models are dependent on one parameter, the bound mass fraction, which we calculate as the self-bound mass in the simulation, as described in the text. We note that since all of these methods are dependent on the bound mass, they are sensitive to the method used for defining bound particles. Also, bound mass calculations include mass that is only temporarily bound, but is leaving the system (e.g. Peñarrubia et al. 2009 ). Most of this temporarily bound mass is at larger radii, which may explain why the mass-loss models all fail to match the bound mass profiles from the simulations beyond 4–5 r unit in Fig. 1 . A more accurate normalization procedure for our model might be to fit the radius enclosing some fraction of the mass, or to fit the peak circular velocity; rather than take either of these approaches, we will later use the mass-loss model in Section 6 to predict theoretically. 5 OUR MODEL ASSUMPTIONS The truncation method described in Section 2 determines which particles will remain bound, and which will be ejected from the system, given a tidal truncation energy . As shown in the previous section, this approach predicts the density (or equivalently the mass or the circular velocity) profiles of the remnants quite well, but appears to be more accurate when mass-loss is slower. Our goal in this section is to understand why this is the case, focusing on the Fast and Slow Simulations described in Section 3 . Suppose we consider a simple model where mass-loss is primarily an energy-based process, as proposed by Choi et al. ( 2009 ). Three main simplifying assumptions are: Mass-loss occurs episodically around the pericentre of the orbit; after each episode the system returns to equilibrium, with the modified spherically symmetric, isotropic distribution function predicted by the energy truncation method. Individual particles are lost or retained based solely on their energy with respect to the rest of the