  We decrease the $rms$ mean curvature and area of a variable surface with a
fixed boundary by iterating a few times through a curvature-based variational
algorithm. For a boundary with a known minimal surface, starting with a
deliberately chosen non-minimal surface, we achieve up to 65 percent of the
total possible decrease in area. When we apply our algorithm to a bilinear
interpolant bounded by four \emph{non-coplanar} straight lines, the area
decrease by the same algorithm is only 0.116179 percent of the original value.
This relative stability suggests that the bilinear interpolant is already a
quasi-minimal surface.
