We have modeled the structure of small bright features, "bright points" seen in an outstanding CH filter (0-band) image. In our model, bright points consist of a Gaussian bright core centered in a Gaussian dark surround. The basis for this approach is the observation that nearly all of the bright points in the image exist within intergranular lanes, vertices between granules, or local brightness depressions. Using reasonable estimates for the size and depth of vertices and lanes, the model predicts that bright points clearly detectable in images with 0".2 resolution will seldom be detectable in images with resolutions beyond 0".4. This occurs because the transfer function of the telescope and atmosphere averages the bright points with their comparably sized dark surroundings to near zero contrast when blurred beyond 0".4. These results explain the great rarity of images that clearly show bright points. Furthermore, the image shows many bright points with core diameters equal to that of the FWHM of a point-spread function of a perfect telescope. If the intensity profiles of these bright points were Gaussian on a flat background, then their intrinsic brightness would have to be unrealistically high and they would not disappear on images blurred beyond 0".4, but would simply gradually expand in size and drop in contrast as the blur increased. Because the bright points are sites of magnetic fields, our model helps to explain lower resolution disk center observations that show magnetic fields occur in regions that are dark relative to the mean continuum level. The modeling also suggests that bright points with diameters of 0".1 or less would be undetectable in the current generation of 0.5 m high-resolution solar telescopes, under any seeing conditions.