Abstract. Noticeable improvements were recently introduced in the modelling of ncapture nucleosynthesis in the advanced evolutionary stages of giant stars (Asymptotic Giant Branch, or AGB, stars). Two such improvements are closely linked together and concern the introduction of non-parameterized, physical models for extended mixing processes and the adoption of accurate reaction rates for H-and He-burning reactions, including the one for the main neutron source 13 C(α,n) 16 O. These improvements profited of a longstanding collaboration between stellar physicists and C. Spitaleri's team and of his seminal work both as a leader in the Nuclear Astrophysics scenario and as a talentscout in the recruitment of young researchers in the field. We present an example of the innovative results that can be obtained thanks to the novelties introduced, by estimating the contributions from a nearby AGB star to the synthesis of short-lived (t 1/2 ≤ 10 Myr) radioactive nuclei which were alive in early Solar System condensates. We find that the scenario indicating an AGB star as the source of such radioactivities, discussed for many years by researchers in this field, appears now to be no longer viable, when the mentioned improvements of AGB models and nuclear parameters are considered.