Summary: We develop a preconditioning strategy based on a non-standard discrete wavelet transform (DWT) for dense non-symmetric linear systems that must be solved when Newton method is used in the solution of elastohydrodynamic lubrication (EHL) problems. Simple band preconditioners and sparse preconditioners based on standard DWT have been found to be of limited value for EHT problems, since they may be singular, give poor convergence or be expensive to apply. We present algorithms for preconditioner design based on detecting non-smooth diagonal bands within an otherwise smooth matrix and applying a non-standard DWT to compress the part of the matrix away from the band. We illustrate, by numerical examples, the improvements that can be made when our methods are used.