Most of the meshes coming from a variety of source are over sampled and exhibit highly irregular connectivity that prevent efficient wavelet analysis. Remeshing comes as a solution to sampling and connectivity optimization with respect to the geometry. The main drawback of existing subdivision remeshing approaches is the lack of control either on the number of triangles or on the geometrical error. We propose a new remeshing scheme that directly produces wavelet-based multiresolution meshes which does not suffer from the previous limitations. We provide a finer control on the resulting number of triangles by using an adaptive subdivision scheme. We also show a lowering of the local resulting geometrical error by using a new curvature-based subdivision criterion.