The authors present a study of an extended (35-power) low-temperature series for the susceptibility of the ordinary two-site three-state Potts model on the square lattice as well as reanalyses of several extant series for the three-site three-state Potts model on the triangular lattice. Dominant and confluent singularities are investigated and the exponents of both are found to be universal and in agreement with known and conjectured exact values.