The thin-phase screen model for ionospheric irregularity perturbations to transionospheric radio propagation is redefined. It is argued that the phase screen normal should be along the line of sight (LOS) between a receiver on the ground and a space transmitter, rather than in the zenith direction at the point of intersection with the LOS, which is traditional. The model is applied to a calculation of TID strength thresholds for the occurrence of multipath and scintillation. The results are in sharp disagreement with the traditional model, which predicts thresholds lower by an order of magnitude in typical cases. Midlatitude observations of TID strengths are reviewed, and it is found that multipath thresholds can be exceeded under one or more favorable circumstances, which include frequencies below about 100 MHz, low elevation angles, winter, night, atmospheric gravity wave velocity near the magnetic field direction and away from parallel with the LOS, and low solar activity.