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Abstract With the aim of pushing the limiting magnitude of interferometric instruments, the need for wide-band detection channels and for a coordinated operation of different instruments has considerably grown in the field of long-baseline interferometry. For this reason, the Center for High Angular Resolution Astronomy (CHARA), an array of six telescopes, requires a new configuration of longitudinal dispersion compensators to keep the fringe contrast above 95% simultaneously in all spectral bands, while preserving the transmission above 85 %. In this paper, we propose a new method for defining the longitudinal dispersion compensators (LDC) suited for multi-band observations. A literal approximation of the contrast loss resulting from the dispersion residues enables us to define a general criterion for fringe contrast maximisation on several bands simultaneously. The optimization of this criterion leads to a simple solution with only two LDC stages per arm and existing differential delay lines, to the glass choice and a simple linear formula for thickness control of all these media. A refined criterion can also take into account glass transmission. After presenting this criterion, we give the optimal solution (medium, configuration) and its expected performance for the planned observing modes on CHARA.