We recently developed a new coarse-grained model of protein structure and dynamics [ Dawid et al. J. Chem. Theory Comput. 2017 , 13 ( 11 ), 5766 - 5779 ]. The model assumed a single bead representation of amino acid residues, where positions of such united residues were defined by centers of mass of four amino acid fragments. Replica exchange Monte Carlo sampling of the model chains provided good pictures of modeled structures and their dynamics. In its generic form the statistical knowledge-based force field of the model has been dedicated for single-domain globular proteins. Sequence-specific interactions are defined by three-letter secondary structure data. In the present work we demonstrate that different assignments and/or predictions of secondary structures are usually sufficient for enforcing cooperative formation of native-like folds of SURPASS chains for the majority of single-domain globular proteins. Simulations of native-like structure assembly for a representative set of globular proteins have shown that the accuracy of secondary structure data is usually not crucial for model performance, although some specific errors can strongly distort the obtained three-dimensional structures.