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tokens: more evident the lower is the observed stellar mass of the galaxy, because of the low chemical enrichment predicted by the more truncated IGIMF. Therefore, the IGIMF does not seem to work in the regions of very low SFR and metallicity typical of UFDs. In the case of CVn I, which is considered more as a dSph galaxy, a short infall time-scale, typical of UFDs, does not allow us to reproduce the cumulative SFH derived by observations, since it predicts a too step rise of the cumulative SFH. However, if a longer infall time-scale is assumed, the MDF and the [α/Fe] abundances are not well reproduced, for both the two IMFs. Therefore we are not able to determine which IMF better reproduces the four observational constraints of this galaxy. More data on this galaxy are necessary before drawing firm conclusions. We are forced to conclude that the models with the Salpeter IMF are able to better reproduce the data than the IGIMF, at least for the version adopted here ( R14 ). Perhaps an IGIMF with a weaker dependence on the SFR and a stronger dependence on metallicity would better fit the properties of these extremely small galaxies. Recently, a new IGIMF has been proposed by Yan, Jerabkova Kroupa ( 2017 ) and Jeřábková et al. ( 2018 ) which enhances the dependence of the slopes of IMF on metallicity, extending it to the low mass range. Such IMF has been applied to the chemical evolution of elliptical galaxies by Yan et al. ( 2019 ). Nevertheless, the models assuming the Salpeter IMF that we have selected as the ones best reproducing the present-day stellar mass match well the [α/Fe] trends but, for a large number of galaxies, they predict too many metal-poor stars than what have been derived by observations. This is similar to the G -dwarf problem but, with the exception of CVnI which has a longer SF episode, it persists even for longer infall time-scales than the one adopted here (τ inf > 0.005 Gyr). The explanation of such a discrepancy could be an observational bias: the samples we have used to build-up the MDFs could be influenced by the instrumentation capability to detect extremely low-metallicity stars because of the weak spectral lines characterizing these stars. Comparing the abundances of UFD stars with the Galactic ones, we suggest that at least a fraction of UFDs could not be the building blocks of the halo given the different [α/Fe] trends observed for UFDs and the Galactic halo. To draw firmer conclusions more data about UFDs are necessary and more elements should be studied such as barium (Spitoni et al. 2016 ). For future projects, it will be interesting to put more stringent constraints on the stellar mass and IMF of UFDs by using photo-chemical evolution models that reproduce at the same time the observed chemical abundances and photometric properties (including the CMD) of UFD stars, taking into account the intrinsic incompleteness of observations (see also Vincenzo et al. 2016 ). Finally, another promising follow-up will be to study