On the site where Arlington County's shiny new county complex sits was once the home of an elderly woman.

When the county first tried to buy the property in the 1950s for its appraised value of $15,000, the woman, then in her seventies, refused to sell. Rather than take her land, county officials waited. And waited.

In 1982, after the woman died, well past her 100th birthday, the county bought the property from her heirs for $358,000.

The story, told in Arlington's official circles, points up just one of the problems faced by this increasingly urban and densely developed county whenever it tries to acquire land for public use.

Not only are county officials loath to seize land from private residents, but when the county does decide to purchase land, the cost can be steep. Land prices have escalated by as much as 23 percent a year during the past decade in some parts of the county. There's also the fact that almost any property the county wants is in somebody's back yard.

Most recently, the county's efforts to find a site for a 68-bed homeless shelter and drug abuse treatment facility have highlighted the county's land acquisition problems. After months of acrimony and citizen outrage, the process is far from over. A county manager-appointed committee stopped short early this month of recommending a site, choosing instead to tap two possible sites in South Arlington and one in North Arlington. Now it remains for County Manager Anton S. Gardner to recommend to the County Board a procedure for choosing and acquiring a single site.

At 25.7 square miles, Arlington is one of the smallest counties in the United States. Eighteen percent of Arlington is owned by the federal government, including Arlington National Cemetery, Fort Myer, National Airport and the Pentagon. In this relatively small space live 157,000 people.

"Most of the land is occupied," said William L. Hughes, director of the department of community planning, housing and development. "People don't come in and say, 'Would you like to buy land for parks or a detox center?' "

At the same time, according to Gardner, there are new pressures driving the need for land. Social problems mean a greater demand for facilities such as group homes and drug treatment centers. And dense development along the corridors of Metrorail, which brings in thousands of workers each day, has created a need for more parks and fire stations.

Official reluctance to use eminent domain adds to the constraints, according to officials and residents familiar with the process.

Where possible, Arlington uses patience instead.

It took almost a dozen years to assemble a block of parkland in the Virginia Square area, according to William W. Taylor, Arlington's real estate supervisor. Since the 1950s Arlington has been acquiring two blocks near the Court House, site of a new government complex and a new jail that is under construction, Taylor said.

Fiscal restraint also limits some of the county's options, said economist John Tuccillo, who serves on Arlington's open space task force and was on the drug treatment center panel.

Noting the county's relatively low real estate tax rate and Triple-A bond ratings, he said Arlington could borrow more through bond financing to acquire land, particularly for parks. "This county is so fiscally conservative. They're almost afraid to do anything," he said.

County Board Chairman Albert C. Eisenberg concedes that the county is conservative.

"We have to gauge what voters are comfortable supporting," he said, noting that one park bond issue in 1979 was turned down by voters. However, voters last month did approve about $4 million in bonds for parkland and a new fire station.

Some analysts have suggested that the current economic downturn and slow real estate market present the county with a good opportunity to buy land.

Hughes, who oversees Arlington's planning, housing and development efforts, calls the suggestions good in theory.

"But the county's running low on money like everyone else," he said.