Abundances of the elements Li, C, N, O and Al, as well as the C-12:C-13 and Mg-24:Mg-25:Mg-26 isotopic ratios, are obtained for 11 barium stars, with the purpose of deriving constraints on the nucleosynthesis event responsible for the chemical peculiarities observed in the envelope of those stars. In particular, the normality of the Mg isotopic ratios and the absence of a large Al overabundance allow us to rule out, in agreement with previous studies, the operation of the Ne-22(alpha, n)Mg-25 reaction as the source of the neutrons necessary for heavy element synthesis. Constraints on the composition of the matter having polluted the barium star envelope can also be derived from the C-12:C-13 and C-12:O-16 ratios. For most barium stars, these ratios are compatible with pollution by matter from cool carbon stars. Some barium stars appear, however, to be C-13-rich, but this conclusion is somewhat dependent on the set of CN lines used to derive the C-12:C-13 ratio. Taken at face values, the low C-12:C-13 ratios deduced from the (CN)-C-12 lines at lambda-8003 and (CN)-C-13 lines at lambda-8004.7 (that are believed to be the most reliable) put interesting constraints on the history of barium stars. It is suggested that, if the accretion of matter from a cool carbon star companion occurs when the barium star is still on the main sequence, the low C-12:C-13 ratios can be reconciled with the carbon overabundance by considering the effect on the first dredge-up of the prior enrichment of the envelope by C-12 from the accreted matter.