Context. The vertical diffusive halo size of the Galaxy, L, is a key parameter for dark matter indirect searches. It can be better determined thanks to recent AMS-02 data.Aims. We set constraints on L from Be/B and Be-10/Be data, and we performed a consistency check with positron data. We detail the dependence of Be/B and Be-10/Be on L and forecast on which energy range better data would be helpful for future L improvements.Methods. We used USINE V3.5 for the propagation of nuclei, and e(+) were calculated with the pinching method.Results. The current AMS-02 Be/B (similar to 3% precision) and ACE-CRIS Be-10/Be (similar to 10% precision) data bring similar and consistent constraints on L. The AMS-02 Be/B data alone constrain

L = 5(-2)(+3)

L =

5

- 2

+ 3

kpc at a 68% confidence level (spanning different benchmark transport configurations), a range for which most models do not overproduce positrons. Future experiments need to deliver percent-level accuracy on Be-10/Be-9 anywhere below 10 GV to further constrain L.Conclusions. Forthcoming AMS-02, HELIX, and PAMELA Be-10/Be-9 results will further test and possibly tighten the limits derived here. Elemental ratios involving radioactive species with different lifetimes (e.g. Al/Mg and Cl/Ar) are also awaited to provide complementary and robuster constraints.