We discuss the use of wavelet bases to solve the relativistic three-body problem in momentum space. We address the treatment of the moving singularities that appear in the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean interaction-independent treatment of the scattering singularities that does not require any subtractions.