Some of the most demanding tests of interface methods for two-phase flows with surface tension which use fixed Eulerian grids occur at the two extremes of highly dynamic flows or static equilibrium conditions. It has been difficult to design an interface method to operate accurately across this spectrum especially for 3D fluid flow calculations which, on the one hand, do not often have the required grid resolution to capture all of the fine scale structures that typically appear in highly stretched interfaces nor, on the other hand, the required accuracy in calculating surface tension forces. We present improvements to the interface reconstruction procedure in the level contour reconstruction method (LCRM) J. Comput. Phys. 180 (2002) 427, which now allow the reconstruction to proceed using a locally instead of a globally calculated contour value. These improvements allow more precise control of the interface reconstruction in highly dynamic flows with coalescence and rupture and also avoid the problem of local mass redistribution in poorly resolved calculations. In addition, a new hybrid technique for surface tension calculation in the context of the front tracking method is demonstrated and shown to result in a marked improvement in suppressing parasitic currents by generally two orders of magnitude. We compare and validate these new procedures in various test cases.