We propose a practical method to construct sparse integer-constrained cone singularities with low distortion constraints for conformal parameterizations. Our solution for this combinatorial problem is a two-stage procedure that first enhances sparsity for generating an initialization and then optimizes to reduce the number of cones and the parameterization distortion. Central to the first stage is a progressive process to determine the combinatorial variables, i.e., numbers, locations, and angles of cones. The second stage iteratively conducts adaptive cone relocations and merges close cones for optimization. We extensively test our method on a data set containing 3885 models, demonstrating practical robustness and performance. Our method achieves fewer cone singularities and lower parameterization distortion than state-of-the-art methods.