We investigate the main physical properties of low-metallicity Asymptotic Giant Branch stars , with the aim of quantifying the uncertainties that presently affect the predicted chemical yields of these stars , associated to mass loss and description of molecular opacities . We find that above a threshold mass , M~ { } \simeq 3.5 ~ { } M _ { \odot } for Z = 0.001 , the results are little dependent on the opacity treatment , as long as hot-bottom burning prevents the surface C/O ratio from exceeding unity ; the yields of these massive AGB stars are expected to be mostly determined by the efficiency of convection , with a relatively mild dependence on the mass-loss description . A much higher degree of uncertainty is associated to the yields of less massive models , which critically depend on the adopted molecular opacities . An interval of masses exists , say 2.0 - 3.0 ~ { } M _ { \odot } , ( the exact range depends on mass loss ) , in which HBB may be even extinguished following the cooling produced by the opacity of C-bearing molecules . The yields of these stars are the most uncertain , the variation range being the largest ( up to \sim 2 dex ) for the nitrogen and sodium yields . For very low-mass models , not experiencing hot-bottom burning ( M \leq 1.5 ~ { } M _ { \odot } ) , the description of mass loss and the treatment of the convective boundaries are crucial for the occurrence of the third dredge-up , with sizable consequences on the CNO yields .