An anisotropic term was added to a successive corrections data assimilation system to reduce the influence across mountain barriers of corrections to the background field that are derived from surface observations. A related change was implemented to reduce the influence of observational corrections across coastal zones and land-lake boundaries. These modifications were tested using the Advanced Regional Prediction System Data Assimilation System (ADAS). Sensitivity tests were conducted on a two-dimensional version of ADAS over the northern Rocky Mountains. Additional tests were conducted for a domain that encompasses the entire western United States. The inclusion of the anisotropic term has improved the analysis by constraining the influence of observations in mountain valleys that may differ from the weather conditions present in adjacent valleys. Rather than propagating surface weather conditions laterally through mountains, this constraint assumes that the background field remains the best choice in regions with relatively little data.