In this paper, we address the problem of capturing both the shape and the pose of a character using a single depth sensor. Some previous works proposed to fit a parametric generic human template in the depth image, while others developed deep learning (DL) approaches to find the correspondence between depth pixels and vertices of the template. In this paper, we explore the possibility of combining these two approaches to benefit from their respective advantages. The hypothesis is that DL dense correspondence should provide more accurate information to template model fitting, compared to previous approaches which only use estimated joint position only. Thus, we stacked a stateof-the-art DL dense correspondence method (namely double U-Net) and parametric model fitting (namely Simplify-X). The experiments on the SURREAL [1], DFAUST datasets [2] and a subset of AMASS [3], show that this hybrid approach enables us to enhance pose and shape estimation compared to using DL or model fitting separately. This result opens new perspectives in pose and shape estimation in many applications where complex or invasive motion capture setups are impossible, such as sports, dance, ergonomic assessment, etc.