We present nucleosynthesis predictions for massive (5-7 M⊙) asymptotic giant branch (AGB) stars of solar metallicity where we delay the onset of the superwind to pulsation periods of P =700-800 days. We found that delaying the superwind in solar metallicity massive AGB stars results in a larger production of s-process elements, something that would be also expected at lower metallicities. These new models and the available observations show that massive C-O core AGB stars in our Galaxy and in the Magellanic Clouds experience considerable third dredge-up (TDU). Thus, if massive AGB stars at the metallicities of the globular clusters (GCs) also experience deep TDU, then these stars would not be good candidates to explain the abundance anomalies observed in most GCs. However, more massive AGB stars (e.g., near the limit of C-O core production) or super-AGB stars with O-Ne cores may not experience very efficient TDU, producing the high He abundances needed to explain the multiple populations observed in some GCs.