A house in a southeast Washington area where break-ins have been on the rise was the site of another sort of misfortune a few days ago when it was heavily damaged by fire. But, police said, they kept that problem from being compounded by burglary.

The fire broke out Nov. 16 in the 4000 block of First Street SE, a neighborhood near the District’s southern tip where police Lt. Mustafa Haamid said there has been “an abnormal increase in burglaries.”

On Nov. 17, police said, an area resident reported a burglary going on at the house that had burned. Knowing the location of the fire, Lt. Haamid said, the officers got there in time to find two men “burglarizing the premises.”

A refrigerator, stove, silverware and copper pipes had been removed, Lt. Haamid said. It was all in the back of the burglars’ pickup truck, he said in an e-mail message.

The two, he said, “were arrested and charged accordingly.”