The nine elements of chemical shielding tensors contain important information about local structure, but the extraction of that information is difficult. Here we explore a semiempirical method that has the potential for providing relatively accessible structural correlations. The approach entails approximating the field-induced electron current density as entirely perpendicular to the applied field. This has two interesting consequences. (1) The resulting shielding tensor is perfectly symmetric. Thus, asymmetry in a shielding tensor is an indication of current density that is not orthogonal to the applied field. (2) The orientation dependence of the chemical shielding at a point of interest is related explicitly to the isotropic average of the chemical shielding at every point in the surrounding region. This suggests a relatively simple relationship between the orientation dependence of the chemical shielding and the molecular structure. Good correlation with experimental tensors is obtained with just one or two adjustable parameters in several series of compounds, including silicates, phosphates, hydrogen bonds, carboxyls, and amides. As expected, the results indicate that for a given center, the contribution to the shielding anisotropy that is associated with each bonded neighbor increases as the number of electrons at either the center or the neighbors increases.