Arbitrary-Lagrangian Eulerian (ALE) approaches are domain-conforming methods specialized in the solution of free-boundary problems (FBPs). ALE methods, in particular those employed with the finite element method, parametrize the weak form by a user-prescribed domain guess that can be mapped into the domain solution by an unknown displacement field. The parametrization results in a fixed-domain problem, nonlinear in displacement, which can then be solved by Newton's method. This approach, although rigorous, has the significant drawback of yielding a problem formulation where displacement is present everywhere inside the bulk of the domain guess, despite not being governed by a physical law therein. This considerably increases the computational size of the problem while further requiring an additional, essentially artificial equation for mathematical closure. In this contribution, an ALE method entitled Total Linearization Method (TLM) that was proposed by Kruyt et al. (International Journal for Numerical Methods in Fluids 1988; 8: 351-363) is extended from the 2D die-swell problem to address general 3D free-surface flow problems. The TLM distinguishes itself from other ALE Newton methods by the fact that linearizing with this approach results in a weak form where displacement is extricated from the bulk of the domain guess and, in turn, present only over the free surface. This significantly reduces the computational size of FBPs, side-stepping the need for solving an artificial governing equation in the bulk as is required by ALE methods. Appropriate preconditioning furthermore boosts the efficacy of the TLM approach; a preconditioner is presented that enables effective numerical solution of linear systems resulting from TLM by iterative solvers, paving the way for efficient and precise solution of steady 3D FBPs with this approach. This research was sponsored by the Swiss National Science Foundation under Advanced Grant Project TMAG-2 209328.