The use of conditional autoregressive (CAR) models for spatial effects is commonplace, especially when dealing with aggregated count data in health studies. CAR models are convenient and relatively easy to implement but suffer from the fact that they have limited flexibility in modeling correlation. We introduce a new CAR model that can accommodate different neighborhood features (including shared neighbors). Further, we examine via simulation how this model performs in comparison with standard CAR models. We also consider the application to a small area health data example.