The first was detonated in a market, followed seconds later by another at a nearby intersection, police said. Mortar rounds also landed in the area as part of an apparently co-ordinated attack, they added.
In the district of al-Utaifiya, a suicide bomber blew himself up in a minibus, killing six people and wounding 10.
"The chances of success [in Iraq] are essentially zero because the Iraqi people have no voice"
Non Sequitur, Cadiz, Spain
Send us your viewsIn Karrada, near the centre of the capital, a car bomb aimed at a police patrol killed five people and wounded another 10 in a blast that rattled windows hundreds of metres away, police said.
The bombings have continued despite Operation Fardh al-Qanoon which saw thousands of Iraqi and US troops deployed in an attempt to return security to Baghdad.
Meanwhile, in Mosul, 390km north of Baghdad, four Iraqi soldiers were killed when two oil trucks driven by suicide bombers exploded outside an Iraqi military base, police said.
"We have seen a rise in the number of car bomb attacks. We have been very diligent in taking down these people who build these car bombs. We are taking one cell at a time," Rear Admiral Mark Fox, US military spokesman, said on Sunday.
The helicopter crash brought the British death toll in Iraq since the US-led invasion in 2003 to 142. Eight have been killed this month alone.
Puma helicopters normally have a three-person crew and can carry up to 16 troops.
Fighters shot down eight helicopters during a month-long period earlier this year, killing 28 people, mainly American soldiers. Six of those aircraft were US military helicopters and the other two belonged to a private American security company.