The Barry administration's plans to improve the housekeeping of city government, making it more efficient and less expensive, are likely to have to start right at home in the District Building.

The city's intergovernmental mail system is so bad that one department head located in the District Building received his notice of a cabinet meeting eight days after the notice was sent from general assistant Ivanhoe Donaldson's office three floors away.

Press secretary Florence Tate once made the mistake of sending administrative aide Lynn Bumbray a news article through the in-house mail system instead of slipping it under the door separating her office from Bumbray's. It took Bumbray two days to get the package.

At one of his cabinet meetings, the mayor stressed the need to cut down on city utility bills, which in some cases are increasing significantly. One of the regular energy drains familiar to many around the District Building is the structure's heating system, which is so archaic that many members of the mayor's cabinet sit in their offices in the dead of winter with the air conditioners turned on to help cool the overheated rooms.

Mayor Barry remains a stanunch advocate of mandatory District residency for all city employes, despite some eyeopening revelations during the great snow of a few weeks back.

When automobile, bus, taxi and subway traffic faltered under the brunt of the snowfall, many suburbanites made it to their government jobs, anyway.

"Actually," said Bary riding through the snow-covered city in his chauffeur-driven sedan, "we've found that some people who live in the suburbs are coming in better than those who live in the District."

Wilhelmina Marshall, executive assistant to budget director Gladys Mack, lives in Marlow Heights, but, said Barry, showed up one morning at 7:30 to prepare for a 9 o'clock meeting. David Stoneburner, a traffic engineer with the Department of Transportation, walked to work from Falls Church, the mayor said.

"We're going to give him a medal," Barry said.

Mayor Barry's personal staff not only lacks Latinos, but also representatives of another group that strongly supported Barry's campaign and has hoped for more influence in the new administration -- gay rights activists.

When a reporter asked press secretary Florence Tate if and when the mayor planned to appoint some gays to his staff, Tate replied, "He may have some now."

"The mayor doesn't go around questioning people's sexual preferences," Tate said. "But you can be sure that the special concerns of gays will be treated sensitively throughout this administration."

Shortly after the mayor's office disclosed the salaries of all its staff members this week, budget director Gladys Mack became one of the most enviable people in D.C. government.

According to figures released by the mayor's office Monday, Mack was the only one of Barry's five city administrators not making $47,500 a year. Her salary was $46,200, even though she had been a city employe longer than the other four administrators.

Apparently prompted by the embarrassing discrepancy between Mack's salary and that of her counterparts, the mayor's office informed Mack the next day she would be given a raise to $47,500, retroactive to Jan. 2 -- the day Barry took office.