In this work we studied the features of the solid-fluid region of computed binary constant-overall-composition phase diagrams (COCPDs), by resorting to calculated constant solidified-fraction curves. As generally done for constant overall composition (COC) mixtures, we computed phase envelopes (made of fluid fluid equilibrium (FFE) and solid-fluid equilibrium (SFE) segments), together with appropriate segments of solid-fluid fluid equilibrium (SFFE) curves. Besides, for achieving a more complete characterization of solid-fluid regions of computed COCPDs, we calculated sets of constant solidified fraction curves. A methodology to find the quantitative connection among these curves and already computed SFFE lines is proposed. The results obtained for heterogeneous regions suggest the existence of complex patterns of behavior, for phase equilibria involving fluid and solid phases. Some of them could be regarded as unexpected. The proposed approach can be applied, in general, to binary systems which present precipitation, in pure form, of the heavy compound.