Story highlights Several inches of rain fell during the day but forecasters were concerned about the potential precipitation overnight

The storm is expected to dump 4 to 8 inches of rain in eastern Texas and Oklahoma

Harris County, Texas, warning: "Bayous and rivers could go out of banks quickly"

(CNN) Tropical Storm Bill hasn't been quite the storm meteorologists anticipated, but it was still bringing significant rain to areas of Texas that have dealt with significant flooding.

Some areas near Houston had nearly 2 1/2 inches of rain Tuesday, the National Weather Service said. Forecasters were concerned that the storm would dump much more rain overnight.

"North side of TS #Bill has strong storms to contend with tonight," the Weather Service's office in Houston tweeted.

There were flash flood warnings for southeastern counties, the last of which was due to end at midnight local time.

The storm system is expected to dump 4 to 8 inches in eastern Texas and Oklahoma, with up to 12 inches in isolated spots in Texas. Western Louisiana and Arkansas are expected to see up to 4 inches of rain.