Goldfarb has already linked to this Foreign Affairs essay on Burma by Michael Green and Derek Mitchell. Still, it's worth pointing out this paragraph in particular:
But China's position could shift, particularly as Beijing considers its longer-term interests. China, like many other states on Burma's border, must be concerned about the effects of its neighbor's tortured development on its own security. In fact, Chinese officials in Beijing and the governor of Yunnan Province, which borders Burma, are reported to have been putting pressure on the SPDC to reform and urgently address drug trafficking and health issues. This quiet shift could track the recent change in Beijing's approach to another wayward neighbor: North Korea. As soon as Beijing realized that being hands-off did not prevent Pyongyang from testing nuclear weapons and ballistic missiles over its objections--thus damaging China's reputation and threatening its security--it agreed to UN Security Council sanctions to try to bring Pyongyang under control.
If that is the case, then it stands to reason that additional pressure on the Burmese regime and highlighting its dependence on Beijing may force the latter to act responsibly in this matter as well.