A group-contribution method for the estimation of Hansen solubility parameters of pure organic compounds is presented. It uses two kinds of characteristic groups: first-order groups that describe the basic molecular structure of compounds and second-order groups, which are based on the conjugation theory and improve the accuracy of predictions. A large variety of characteristic groups ensure the prediction of Hansen solubility parameters for a broad series of organic compounds, including those having complex multi-ring, heterocyclic, and aromatic structures. The predictions are exclusively based on the molecular structure of compounds, and no experimental data are needed. The predicted values permit a fairly reliable selection of solvents based on the radius of a Hansen solubility parameter sphere or on a Teas parameter ternary plot. Especially designed algorithms permit the preparation of a list of new molecular structures which, if synthesized, could be the ideally suited solvents for a series of corresponding applications.