The modeling power of the method of linear combinations of connectivity indexes (LCCI), based on a minimal and on an expanded set of connectivity indexes, has been tested on several properties of different classes of organic compounds : the melting points and motor octane numbers of alkanes, the melting points and solubilities of caffein homologues, and four different physicochemical properties of organophosphorus compounds. The modeling of the first property, a classical shape-dependent property and up to date a challenging problem of molecular modeling, was resolved by partitioning the entire set of alkanes into congruent subsets. A minimal set of normal and valence connectivity indexes was able to model the melting points of caffein homologues that have quite similar molecular shapes and sizes, while the modeling of the solubilities of these homologues was unravelled by taking into consideration their association in solution and by employing linear combinations of squared connectivity indexes. The very effective modeling of the two different types (shape- and size-dependent) of properties of the organophosphorus compounds, with a minimal set of connectivity indexes, delineates also a test for the proposed valence delta(v) value of phosphorus in organophosphorus derivatives. Linear LCOCI combinations of orthogonal connectivity indexes were also tested to improve, if possible, the modeling of the properties of the given classes of compounds. Modeled properties show that the connectivity indexes can be highly dependent on the detailed knowledge of the physicochemical state of the investigated system and that, usually, LCCIs with a minimal basis set yield quite adequate modeling.