We present and analyse low-temperature series and complex-temperature partition function zeros for the q-state Potts model with q = 4 on the honeycomb lattice and q = 3,4 on the triangular lattice. A discussion is given on how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with q = 3 on the honeycomb lattice and with q = 3,4 on the kagomé lattice.