The problem of thermal escape is considered in which the effects of both thermospheric winds at the exobase and collisions below the exobase are included in a Monte Carlo calculation. The collisions are included by means of a collisional relaxation layer of a background gas which models the transition region between the exosphere and the thermosphere. The wind effects are considered in the limiting cases of vertical and horizontal flows. Two specific species are considered: terrestrial hydrogen and terrestrial helium. In the case of terrestrial hydrogen the escape fluxes were found to be strongly filtered or throttled by collisions at high exospheric temperatures. The ratio of escaping flux to total upward flux at the exobase is found to approach a limiting value of significantly less than unity. Collisional filtering of particles exceeding the escape velocity greatly reduces the enhanced H escape that would otherwise be produced by winds. Such a drastic reduction in escape by collisions occurs even for winds near the sound speed. For terrestrial helium, departures from previous predictions for collisionless wind enhanced escape are found to be insignificant at exospheric temperatures of less than 5000 ¿K. Thus, even with collisions, wind enhanced escape could be a significant helium loss mechanism contributing to the helium budget. In the case of terrestrial hydrogen the mass of the background gas comprising the relaxation layer is varied from 1 to 44 amu. The result is increased throttling with increasing background mass, the effect being larger at lower temperatures. Finally, the model is applied to molecular hydrogen diffusing through a methane relaxation layer under conditions possible on Titan. The results are similar to the case of terrestrial hydrogen, with wind enhanced escape being strongly suppressed by collisions. It is concluded that wind enhanced escape is not an important process on Titan.