Mayor-Elect Sharon Pratt Dixon, who has pledged to slash city spending when she takes office, may find she is unable to take the ax to the D.C. Department of Corrections.

That department, which was a modest $59 million operation 10 years ago, has become one of the city's biggest and most expensive agencies, and administration officials expect its costs to climb even more in coming years.

Last year, the corrections budget rose to $216.8 million, an increase of 58.8 percent over the previous five years. Its budget for the year ending Sept. 30 is $252.7 million, making it the fourth-largest item in the D.C. budget. Only the human services and police departments and schools spend more.

A member of Dixon's transition team who studied the corrections department said the rising costs have less to do with the waste and personnel bloat sometimes attributed to city agencies than with the drug epidemic.

Corrections Director Walter B. Ridley is being forced to respond to the rapidly rising inmate population while his agency operates under several severe court orders requiring specific, multimillion-dollar expenditures for inmates and establishing population limits at some institutions.

Given the fact that judges influence large portions of the corrections budget, Dixon will have few options to cut staff and programs there, city officials said. Dixon aides looking at corrections are struck by that lack of fiscal maneuvering room, not by the kinds of management problems they've uncovered in other city agencies.

"We found that, under the circumstances, the Department of Corrections operates very well. That's unusual," said Shahid Abdullah, a member of the Dixon transition team's subcommittee that studied corrections.

Even Mayor Marion Barry's Rivlin Commission, which sharply criticized spending in other city agencies, said there are no easy, immediate ways to cut costs substantially in the beleaguered corrections department.

"The fiscal obligation of the District for corrections will continue to increase with rising capital and operating requirements," said the commission, chaired by former Congressional Budget Office chief Alice M. Rivlin.

The rising costs are largely a ripple from the drug epidemic. Large numbers of drug arrests by the D.C. police, and mandatory sentencing guidelines aimed at keeping offenders confined for longer periods, have helped to increase the city's prison population dramatically.

The District's prison capacity has been expanded by 24 percent over the last five years, but that has not kept pace with the rising inmate population. A decade ago, the inmate head count stood at about 3,800. Today, the corrections department is responsible for 9,926 people in confinement. The department projects that, at the current rate of increase, the population will be 19,000 by 1996.

Of the more than $216 million the District spent in 1989 on the city jail in Southeast Washington and seven facilities on 3,000 acres at the Lorton complex in Fairfax County, $150 million was used to house, feed and educate inmates.

A considerable portion of the department's budget, however, is under the sway of the federal courts because of lawsuits filed on behalf of inmates alleging crowded, dirty and unsafe conditions.

According to the Rivlin Commission, the department had to earmark about 13 percent of its 1990 budget, or $31 million, on court-ordered prison construction and fines for disobeying court orders involving inmates.

Corrections officials are taking several short-term measures to address the court orders and alleviate crowding -- including contracting with prisons elsewhere to house inmates.

Those arrangements are costly. In 1989, the city government paid more than $27 million to the Federal Bureau of Prisons to house city prisoners. The department estimated it will pay 20 percent of its $252.7 million budget this year to the federal prisons and other states to house prisoners.

Corrections officials said it would be cheaper for the District in the long run to build and operate its own facilities. Long-range plans include building an 800-bed "Correctional Treatment Facility" to provide intensive services for substance abusers and inmates with emotional problems. Those plans also call for a new 1,000-bed medium-security facility at Lorton and a 1,500-bed detention facility in the District.

Those new facilities will require more staff members, and consequently more dollars. Prison officials estimate they will need to hire several hundred people for the treatment facility alone.

Unlike other prison systems, where the corrections load is distributed among local, county and state governments, the D.C. department carries the burden alone.

Dixon aides, prison experts and D.C. Council members said the monumental challenges facing the new administration will require new and creative approaches to corrections.

One result may be that court authorities and politicians move away from warehousing inmates and endorse "front end" initiatives, such as crime prevention and inmate training, prison and administration officials said.

Some D.C. Council members who supported measures requiring mandatory sentences for some crimes said they may soften their hard-line stance on crime and punishment. Council member H.R. Crawford (D-Ward 7) noted that the council is considering legislation to provide drug treatment as an alternative to incarceration in drug-related cases.

"The society is going to have to take a different approach toward treating those persons who are drug abusers," he said. "It costs less to treat a person, and the payoff is greater."

In any case, the executive in charge will be a man well versed in the corrections budget crunch. Dixon recently asked Ridley to remain in her Cabinet -- one of the few ranking Barry administration officials she has kept on board.