A spate of bombings in Baghdad killed three people, including a police officer and an army soldier, and wounded 20, police officials have said.
The strikes came a week before all but 50,000 US troops leave Iraq - a military drawdown that has raised fears the country's already shaky security will become even less safe.
Baghdad police said unknown attackers in a speeding car threw the grenade in the mixed Sunni-Shiite neighbourhood of New Baghdad in the capital's east on Monday.
The blast killed one policeman and wounded another, a city police official said. A medic at Baghdad's Ibn Al-Nafees hospital confirmed the casualties.
On Sunday, a grenade attack on an Iraqi army checkpoint in Amariyah, a Sunni area in western Baghdad, killed one soldier and injured two others around 11 pm, police and hospital officials said.
Earlier, a shop selling alcohol near central Baghdad was targeted by a roadside bomb that wounded two people. An hour later, another bomb struck a popular cafe in the capital's southwest. A policeman said the explosion killed one person and wounded 15. A medic at the city's Yarmouk hospital confirmed the casualties.
All officials spoke on condition of anonymity because they were not authorised to talk to the media.