Background. The slope (SII) and relative (RII) indices of inequality are commonly recommended to monitor health inequality policies. As an upwards shift of the educational level distribution (ELD) can be part of those policies, we examine how such a shift affects the SII, the RII and the population attributable fraction (PAF). Methods. We simulated 632 distributions of 4 educational levels (ELs) by varying the share (p1 to p4) of each EL, with constant mortality rates (MR) and calculated the corresponding RII, SII and PAF. Second, we decomposed the effect on the three indices of a change affecting both the ELD and the MRs, into the contributions of each component. Results. RIIs and SIIs sharply increase with p4 at fixed p1 values and evolve as reversed U-curves for p1 changing in complement to p4. The RII reaches a maximum, at much higher p4 values than the SII. PAFs monotonically decrease when p4 increases. Conclusion. If improving the educational attainment is part of a policy, an upwards shift of EL should be assessed as a progress; however the RII, and to a lesser extent the SII, frequently translate an increased EL4 share as a worsening. We warn against the use of SII and RII for monitoring inequality-tackling policies at changing socio-economic structures. Rather, we recommend to complement the assessment of changes in absolute and relative pairwise differentials, with changes in PAF and in the socio-economic group shares.