We describe recent developments in the method of fluctuation splitting, in particular the minimization of residuals with respect to both the nodal values of the solution and also the nodal co-ordinates. For elliptic problems, including external (lifting) flows, obtaining good results requires that the residuals be evaluated to third order. Solutions to typical airfoil problems can then be obtained with very economical grids. For hyperbolic problems, only a second-order evaluation of the residual is needed. Shocks can be incorporated with arbitrarily high resolution by allowing elements to shrink to zero area, but to exclude the possibility of rarefaction shocks an adaptive quadrature must be employed. Copyright © 2002 John Wiley & Sons, Ltd.