Abstract We present model occultation lightcurves demonstrating that a strong thermal inversion layer at the base of Pluto's stratosphere can reproduce the minimum flux measured by the Kuiper Airborne Observatory (KAO) during the 1988 occultation of a star by Pluto. The inversion layer also forms the occultation equivalent of a mirage at a radius of 1198 km, which is capable of hiding tropospheres of significant depth. Pluto's surface lies below 1198 km, its radius depending on the depth of the troposphere. We begin by computing plausible temperature structures for Pluto's lower atmosphere, constrained by a calculation of the temperature of the atmosphere near the surface. We then trace rays from the occulted star through the model atmosphere, computing the resultant bending of the ray. Model light curves are obtained by summing the contribution of individual rays within the shadow of Pluto on Earth. We find that we can reproduce the KAO lightcurve using model atmospheres with a temperature inversion and no haze. We have explored models with tropospheres as deep as 40 km (implying a Pluto radius of 1158 km) that reproduce the suite of occultation data. Deeper tropospheres can be fitted to the data, but the mutual event radius of 1150 km probably provides a lower bound. If Pluto has a shallow or nonexistent troposphere, its density is consistent with formation in the solar nebula with modest water loss due to impact ejection. If the troposphere is relatively deep, implying a smaller radius and larger density, signficant amounts of water loss are required.