Phonon drag thermopower S_g calculations are presented for a quasi-2D electron gas at the (100) plane in a Si MOSFET and compared with previous theory and experiment. Without screening -S_g is improved to a factor of approximately 16 times larger than experiment (from approximately 35). Multi-sub-band screening is considered and its importance assessed in the experimental range (2-6 K and electron densities to 10¹⁶ m^-2) but a single sub-band approximation is found to be sufficient and gives thermopowers just approximately 40% different from experiment. Further improvement is made by adopting the Fang and Howard variational wavefunction and better material parameters. The best agreement is found to be about 5% at temperatures in the mid-range (4 K) and for the highest electron densities. The same excellent qualitative agreement with experiment is retained including the peak in -S_g/T³ whose presence is explained by enhanced phonon absorption around the Kohn resonance (q approximately=2k_F). The peak positions move up in temperature (by about 0.75 K) because the dominant q-value increases and reduces the effect of screening on S_g at higher T. In GaAs/GaAlAs heterojunctions S_g is much less sensitive to screening effects because the screening constant is much smaller in GaAs than it is in Si.