Bacterial cells often suffer a fitness cost after conjugative plasmids’ entry because these cells replicate slower than plasmid-free cells. Compensatory mutations may appear after tens of or a few hundred generations, reducing or eliminating this cost. A previous work based on a mathematical model and computer simulations has shown that plasmid-bearing cells already adapted to the plasmid may gain a fitness advantage when plasmids transfer into neighboring plasmid-free cells because these cells are still unadapted to the plasmid. These slow-growing transconjugants use fewer resources, which can benefit donor cells. However, opportunities for compensatory mutations in transconjugants increase if these cells become numerous (through replication or conjugation). Moreover, transconjugants also gain an advantage when transferring the plasmid, but the original donors may be too distant from conjugation events to gain an advantage. To understand which consequence prevails, we performed further computer simulations allowing versus banning transfer from transconjugants. The advantage to donors is higher if transconjugants do not transfer plasmids, mainly when donors are rare and when the plasmid transfer rate (from donors) is high. These results show that conjugative plasmids are efficient biological weapons even if the transconjugant cells are poor plasmid donors. After some time, conjugative plasmids gain other host-benefit genes, such as virulence and drug-resistance.