Analytical results show that three shape velocity parameters for a given tangential wind maximum of the non-Rankine vortex have an important modulating influence on the behavior of realistic tangential wind and corresponding pressure deficit profiles. The first parameter, changing from a sharply to broadly peaked wind profile spanning the maximum, decreases the corresponding pressure profile and hence the central pressure minimum. The second (third) parameter modifies the pressure profile by varying the inner (outer) wind profile inside (outside) the radius of the maximum, and hence the pressure minimum. When comparing to the non-Rankine tangential wind and pressure deficit profiles, the Rankine tangential wind profile is overestimated, and the corresponding pressure deficit is underestimated. This suggests that the Rankine model is not a good starting point for the examination of the atmospheric pressure structure within any non-Rankine vortex because the tangential wind profile's unrealistic cusp at the radius of the maximum remains unchanged and is not able to match the continuous wind maximum, as commonly seen in various observations.