Various interaction techniques have been studied for providing the feeling of touch and improve immersion in augmented reality (AR) environments. Tangible AR interaction exploiting two types (product-type and pointer-type) of simple objects has earned great interest for cost-effective design evaluation of digital handheld products. When the sizes of markers attached to the objects are kept big to obtain better marker recognition, the pointer-type object frequently and significantly occludes the product-type object, which deteriorates natural visualization and level of immersion in an AR environment. In this paper, in order to overcome such problems, we propose tangible AR interaction using fingertip touch combined with small-sized markers. The proposed approach facilitates the use of convex polygons to recover the boundaries of AR markers which are partially occluded. It also properly enlarges the pattern area of each AR marker to reduce the sizes of AR markers without sacrificing the quality of marker detection. We empirically verified the quality of the proposed approach, and applied it in the process of design evaluation of digital products. From experimental results, we found that the approach is comparably accurate enough to be applied to the design evaluation process and tangible enough to provide a pseudo feeling of manipulating virtual products with human hands.