Observations indicate that some of the largest Kuiper Belt Objects (KBOs) have retained volatiles in the gas phase (e.g., Pluto), while others have surface volatiles that might support a seasonal atmosphere (e.g., Eris). Since the presence of an atmosphere can affect their reflectance spectra and thermal balance, Schaller & Brown examined the role of volatile escape driven by solar heating of the surface. Guided by recent simulations, we estimate the loss of primordial N-2 for several large KBOs, accounting for escape driven by UV/EUV heating of the upper atmosphere as well as by solar heating of the surface. For the latter we present new simulations and for the former we scale recent detailed simulations of escape from Pluto using the energy limited escape model validated recently by molecular kinetic simulations. Unlike what has been assumed to date, we show that unless the N-2 atmosphere is thin (< similar to 10(18) N-2 cm(-2)) and/or the radius small (< similar to 200-300 km), escape is primarily driven by the UV/EUV radiation absorbed in the upper atmosphere. This affects the discussion of the relationship between atmospheric loss and the observed surface properties for a number of the KBOs examined. Our long-term goal is to connect detailed atmospheric loss simulations with a model for volatile transport for individual KBOs.