A recently developed method for recovering two-dimensional (∂/∂z ≈ 0), time-stationary magnetic field structures in the magnetopause is improved and further applied to two complete magnetopause crossings by the spacecraft AMPTE/IRM. The technique consists of solving the Grad-Shafranov (GS) equation for magnetohydrostatic structures as a Cauchy problem, using measured data along a spacecraft trajectory through the structure as spatial initial values. We have implemented the following improvements: (1) allowing for different functional behavior of the transverse pressure, Pt = p + Bz2/2¿0, versus A, the calculated magnetic potential, on the magnetosphere and the magnetosheath side of the magnetopause; (2) allowing for change in the velocity of the magnetopause structures as they move past the spacecraft by using a time-varying deHoffmann-Teller (HT) frame velocity; (3) suppressing numerical instabilities and thus extending the integration domain by constraining the behavior of the total pressure. Results from two AMPTE/IRM events show layered and asymmetric structures on the two sides of the magnetopause owing to double-branched behavior in p(A) as well as Bz(A). A time-varying HT frame results in a curved spacecraft trajectory through the magnetopause. The reconstructed field structures show important changes in size but only slight changes in configuration. The use of a time-varying HT frame for determination of time-varying magnetopause motion is discussed.