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The classical fencing problem occurs in radiant heat-transfer computations when a surface extends from one compartment to another, with the two compartments otherwise exchanging little heat. The surface that separates the two compartments is called a “fence.” If the gap between the bottom of the fence and the surface that extends under the fence is small, the potential for a large fencing error is evident from an examination of the drawings. In large models, with many surfaces forming many compartments, the fencing error is less evident. In this paper we examine the fencing errors in two prototype geometries. If the fenced surface is adiabatic, the error is found to be significant for surprisingly large gaps. A surface can be adiabatic due either to a high reflectance or a layer of insulation. The error is found to become insignificant when there is no reflectance.