via China Digital Times, it seems that the People's Republic is innovating in the fight against Muslim insurgencies:
Ironically, China’s ability to successfully kill or capture militants without social blowback demonstrates the significant degree to which China has won the population’s “hearts and minds,” however begrudgingly....
However, success came as China reduced the brutality of its repression and pulled the military out of direct confrontation with society. China built up more restrained, effective, and specialized police forces and tactics and reinvigorated political and educational projects in Xinjiang. The Chinese government purged separatist sympathizers from local governments and attempted to remove political dissent from religious worship. At the same time, availability of Uyghur language education was broadened and Beijing sought to expand economic development in Xinjiang, which was viewed as the key to success. Uyghurs in Xinjiang repeatedly explained in interviews that these changes made participation in the Chinese state more attractive, despite perceptions that economic opportunities primarily benefited the Chinese.
It was a lot more comforting when we could rely on the Communists to be the slow learners in the global classroom. But here we've got the Chinese government not only -- gasp! -- acknowledging and working to resolve Muslim grievances, but even repudiating the iron-fisted military approach to counter-terrorism:
The massive 1997 Yining riot involving over 1,000 Uyghurs, in which over 150 reportedly died from security force excesses, has not been repeated. While there has been ongoing low-level violence in Xinjiang since 9/11, Chinese government claims that this is the result of Uyghur separatists are suspect. China’s initial actions were brutal, and credible reports of security force excesses and torture persist. However, success came as China reduced the brutality of its repression and pulled the military out of direct confrontation with society. China built up more restrained, effective, and specialized police forces and tactics and reinvigorated political and educational projects in Xinjiang.
Now, obviously not all of these means are available to the US when the war is nominally about democracy-building, especially the mention of depoliticizing worship. But the key to the CCP's success, at least according to this article, was the construction of peaceful, and effective, modes of civil engagement for the Uyghur community. Uyghurs are being welcomed in to the actually-existing and actually-functional Chinese government and economy, at least at the local levels. No such options exist in Iraq today, locally or nationally.