Back in 2008 they peaked with around 6-8 rockets per day fired at the Embassy (then in the Republican Palace) from Sadr City.
Iran has a few different options to choose from in Iraq, to get someone to pop a few rockets for them. They could even send their own guys in to do it themselves, if they wanted.
I know what you mean!
2004 Karshi-Khanabad/Kandahar Taliban
2005 Dubai/Kandahar Taliban
2006 Baghdad/Al Qaim Sunni
2007 Baghdad/Al Asad combo
2008 Baghdad/Al Asad combo
2009 Baghdad/Al Kut Shia