I often hear about the Taliban's short-lived ban on opium cultivation in 2000, but according to this paper (pdf), the ban likely had nothing to do with religion, morals, or international pressure:
Under the ban, poppy cultivation was reduced by more than 90 percent; it continued to flourish only in areas controlled by the anti-Taliban Northern Alliance forces.
Though the West initially applauded the Taliban’s about-face as a sign of a new willingness to join the international community, the enthusiasm was probably premature. Analysts now believe that the Taliban had a large stockpile of opium and heroin on hand from previous years of bountiful production, and that the ban was simply an attempt to use Afghanistan’s monopoly power to raise prices in a weak market.
It looks likely only a profit motive can stop Afghanistan's heroin exports.