Visual elements such as grids, labels, and contour lines act as “reference structures” or “visual metadata” that support the primary information being presented. Such structures need to be usefully visible, but not so obtrusive that they clutter the presentation. Our goal is to determine the physical, perceptual and cognitive characteristics of such structures, ideally in a way that enables their automatic computation. We present the result of a set of experiments to determine effective display ranges, described in terms of transparency (alpha), for thin rectangular grids over scatterplot data. These show that an effective range can be defined in terms of alpha. In an effort to create a display-independent set of metrics, we analyze these results in terms of luminance contrast, with mixed results. We conclude that the appearance of transparency is an important aspect of subtle visualization.