In Mahmudiya, located in the notorious "triangle of death" just south of the capital, six mortar rounds rained down on three houses, killing four people and wounding 13 on Saturday.
Another four Iraqis were killed earlier when a roadside bomb exploded near a bus travelling through the eastern edge of the city, police reported.
The blast also wounded two others on the bus, which was passing through a mixed Sunni-Shia part of the city. Armed men in the same neighbourhood attacked a police checkpoint, gravely wounding one policeman.
A Sunni imam was shot dead in the Hay al-Amal neighbourhood in southern Baghdad, while two civilians, a man and a woman, were killed in a crossfire between police and assailants in the western Amiriya neighbourhood.
Teenage boys killed
In the small town of Balad Ruz, east of Baghdad near the Iranian border, a roadside bomb killed two teenage boys selling farm produce from the back of their bicycles.
A passing car was also hit, but the three occupants were only injured.
Ten more corpses were also discovered in Baghdad, bringing the number of bodies, most showing signs of torture, discovered by police over the last week to about 75.
Bound corpses shot in the head or bearing marks of torture are turning up on a daily basis in Baghdad and are believed to be the results of tit-for-tat killings between Sunnis and Shias in an environment of increased sectarian strife.