A spate of bombing attacks in Baghdad killed three people and wounded 20, police officials said Monday.

The strikes came a week before the deadline for all but 50,000 U.S. troops to be out of Iraq — a military drawdown that has raised fears the country's already shaky security will worsen.

In one of the bombings, Baghdad police said unknown attackers in a speeding car threw a grenade in the mixed Sunni-Shiite eastern neighborhood of New Baghdad around 6:30 a.m. 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.

Late Sunday, a grenade attack on an Iraqi army checkpoint in Amariyah, a Sunni area in western Baghdad, killed one soldier and injured 2 others around 11 p.m., police and hospital officials said.

Earlier, a liquor store near central Baghdad was targeted by a roadside bomb that wounded two people around 8 p.m. An hour later, another bomb struck a popular cafe in the capital's southwest. A policeman said that explosion killed one person and wounded 15 people. A medic at the city's Yarmouk hospital confirmed the casualties.

All officials spoke on condition of anonymity because they were not authorized to talk to the media.