Abstract. Accurate relative abundances have been obtained for carbon, oxygen, sodium, aluminium, silicon, and calcium in a sample of mildly metal-poor stars. This analysis complements a previous study carried out by Jehin et al. (1999, A&A, 341, 241), which provided the basis for the EASE scenario. This scenario postulates that field metal-poor stars were born in selfenriched proto-globular cluster clouds. By further investigating the correlations between the different α-element abundances, we propose a modified scenario for the formation of intermediate metallicity stars, in which the stars exhibiting lower than average α/Fe abundance ratios would form in low mass clouds, unable to sustain the formation of very massive stars (M > ∼ 30 M ). Moreover, the carbon-to-iron ratio is found to decrease as one climbs the so-called Population IIb branch, i.e. when the s-element abundance increases. In the framework of the EASE scenario, we interpret this anticorrelation between the carbon and the s-element abundances as a signature of a hot bottom burning process in the metal-poor AGB stars which expelled the matter subsequently accreted by our Population IIb stars.