A projection augmented model (PA model) is a type of haptic augmented reality display. It consists of a real physical model, onto which a computer image is projected to create a realistic looking object. Thus, a PA model creates the illusion of actually being the object that it represents, as opposed to a white model and a projected image. Users can physically touch the surface of a PA model with their bare hands, which has experiential value for the types of applications for which they are being developed. However, the majority of PA models do not provide haptic feedback for material properties such as texture, and hence feel incorrect when they are touched. In addition, most PA models are front-projected which means the projected image appears on the back of the user's hand, and their hand casts a shadow on the display. Previous research has found that touching this type of PA model reduces a user's sense of object presence. The empirical study reported in this paper investigated which of the problems had a greater effect on object presence. It was found that object presence was significantly higher when correct haptic feedback for materia properties was provided; however eliminating the visual projection problems rarely affected object presence. These results have implications for the direction in which PA model technology should be developed. They also have implications for theory on how the haptic and visual senses contribute to a person's sense of object presence, and indeed presence.