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The parallel tangent method widely applied to predict the composition and driving force to form a nucleus from an oversaturated solution is extended in this paper. The parallel tangent method is shown to (i) Over-estimates the composition difference between the first nucleus and the parent phase, (ii) Neglects the composition dependence of interfacial energies and (iii) Neglects the composition dependence of probability to form embryos prior to nucleation. New model equations are developed here for the composition dependence of the interfacial energies and probability to form the embryos as function of nucleus composition at given matrix composition. The most probable composition of the first nucleus is found at the maximum of the driving force of nucleation extended by the new model equations. The success of the extended method is demonstrated for an Al-Fe liquid alloy with 0.3 w% of Fe to predict the first nucleating intermetallic phases upon cooling after nucleation of the fcc phase. It is shown that although the prediction based on the parallel tangent method contradicts experimental observations, the prediction based on our extended method agrees with them. [ABSTRACT FROM AUTHOR]