Accepted —-. Received —-; in original form —-ABSTRACT The most massive elliptical galaxies apparently formed the fastest, because the ratio of α elements (such as oxygen) to iron is the smallest. In fact, iron is mainly pro-duced from type Ia supernovae on a timescale of ∼ 0.1 − 1 billion years, while the α elements come from massive stars on timescales of a few tens of million years (Mat-teucci 1994). Reproducing such a α/Fe correlation has long been a severe problem for cosmological theories of galaxy formation, which envisage massive galaxies to assem-ble gradually from smaller progenitors, and to be characterized by a star formation history too much extended towards late cosmic times. While it has recently become clear that feedback from Active Galactic Nuclei (AGN) activity play a role in the late quenching of star formation (e.g. Cattaneo et al. 2009), and that early star formation history in the galaxy progenitors affect the α/Fe ratio (Calura & Menci 2009), major mergers alone cannot enhance the star formation in the high-redshift progenitors to the levels required to match the steepness of the observed α/Fe correlation (Spolaor et al. 2010). Here we report that the inclusion of the effects of fly-by 'harassments', that trigger lower level starbursts, combined with the AGN quenching of the starburst activity, considerably enhances the capability to account for the observed α/Fe ratio in ellipticals within cosmological galaxy formation models . The critical difference be-tween the earlier work and the present result is the effect of starbursts driven by fly-by encounters that would have been very common amongst the high-redshift progenitors of massive galaxies and which would have boosted star formation in the first 2 billion years after the Big Bang, combined with quenching of the burst activity within the first 3-4 Gyr.