Matrix-free implicit treatments are now commonly used for computing compressible flow problems: a reduced cost per iteration and low-memory requirements are their most attractive features. This paper explains how it is possible to preserve these features for all-speed flows, in spite of the Use of a low-Mach preconditioning matrix. The proposed approach exploits a particular property of a widely used low-Mach preconditioner proposed by Turkel. Its efficiency is demonstrated on some steady and Unsteady applications. Copyright (C) 2008 John Wiley & Sons, Ltd.