Previous attempts to model elevated-pressure coflow laminar flames have been hindered by neglecting the preheating within the burner, caused by downward heat transfer to the burner. In the present work, the computational domain is extended below the exit plane of the fuel tube to account for the flame preheating effect. Conjugate heat transfer (CHT) is implemented by the harmonic mean method to model the heat transfer between the fluid streams and solid fuel tube. This extension of the domain allows for solutions to a high pressure ethane/air data set from 2 to 33atm, which is an improvement over previous attempts where only pressures below 15atm could be modeled. The extended model more accurately predicts centerline soot formation than the truncated model due to capturing fuel pyrolysis that occurs below the exit plane of the fuel tube. This increased fuel pyrolysis increases the contribution by polycyclic aromatic hydrocarbon (PAH) condensation to computed soot volume fractions. For pressures above 20atm, the extended model predicts that PAH condensation is the dominant mechanism on the wingsa location where surface growth was thought to be heavily dominant regardless of flame characteristics. It is determined that the choice of fuel tube wall treatment does significantly affect numerical predictions, with the best experimental agreement obtained using a CHT model as oppose to an isothermal or adiabatic walls. The extended model with CHT is the only model that displays quantitative accuracy and is a significant advancement over previous qualitatively accurate models. [Supplementary materials are available for this article. Go to the publisher's online edition of Combustion Science and Technology for the following free supplemental resource: Numerical details.]