So far, the U.S. “surge” in Iraq has focused largely on the Sunni militants who make up the bulk of the anti-U.S. insurgency. But now, the Los Angeles Times reports, U.S. and Iraqi government forces are coming under pressure from Sunni politicians to go after what many have thought was the main target of the escalation: the Shiites who make up the Mahdi Army.

Led by radical Shiite cleric Muqtada al-Sadr, who was one of the first to speak out against the U.S. occupation, the Mahdi Army’s stronghold is in the section of Baghdad that was once named Saddam City. Today, reflecting the shift in power since the invasion, that area of 2 million Shiites is now Sadr City.

U.S. forces have tried to quell the anti-U.S. militants in Sadr City once before, in 2004. That operation resulted, the Times says, only in heavy casualties for the U.S. and a bolstering of Sadr’s popularity.

Today, Sadr City — despite the presence of the Mahdi Army — is one of the calmest areas of Baghdad. That’s one of the reasons some would like to avoid entering it as part of the security crackdown, fearing a return of the earlier troubles there. Additionally, Sadr and his supporters make up one of the key constituencies of the government of Iraqi Prime Minister Nouri al-Maliki; if Sadr were to withdraw that support, Maliki’s government might well collapse. Finally, as Salon has previously reported, one problem with moving against the Mahdi Army is that there is a significant extent of Mahdi Army sympathy within the Iraqi army itself.