THE DISTRICT of Columbia, wracked by the trauma of Marion Barry's self-destructive conduct and the impossible costs of the huge, unresponsive bureaucracy that he fashioned over the years, is in desperate need of fresh air and ideas at city hall. A new mayor is coming for sure, and that in itself is good. And compared to the fields of candidates running in other cities and towns, the choices for Washington are impressive: they are knowledgeable, well-schooled and aware of the special services required for the urban poor.

But the legacy of Marion Barry's last years as mayor demands dramatic change in the way city hall does -- and doesn't -- do business. The local government has gone off the tracks in the past six years and is now heading into deep financial trouble. Tax burdens are heavy, but corresponding improvements in government services are few, and debt continues to loom. The government is on a treacherous course that calls for a leader with exceptional courage, intellect, instincts -- the ability to say candidly what is wrong and to recognize and attract fresh top talent to rebuild the broken machinery at the District Building. The candidate in the best position to make the necessary difference is the one who is clear of responsibility for the erosion at city hall: Sharon Pratt Dixon.

Mrs. Dixon has guts. She was the first major city figure to call for Mayor Barry's resignation, and she was right. She was the first candidate to say that thousands of local government jobs must be trimmed, and she was (and is) right about that too. The next mayor, faced with critical financial trouble, will have to make painful and sometimes unpopular choices. Why not vote for someone whose campaign has shown she can do so?

For us it came down to a choice between Mrs. Dixon and council member John Ray. Mrs. Dixon is untested as an elected public administrator -- although council members do not administer large operations either -- and polls so far show her a long shot. Mr. Ray, a veteran at-large legislator with broad organizational support and solid financial backing has been comfortably in first place in every poll taken to date. His ability to mount this strong campaign -- running through the ranks of business, labor, church groups and the grass roots -- says something about his ability to balance coalitions and interests. He also offers a welcome difference in style from that of Mr. Barry.

But finally, for us, the down side of Mr. Ray's particular talent was this invincibly accommodative instinct: in an emergency, an extraordinary situation such as the District faces, it often means that you can't be strict enough with those you must disappoint. Mrs. Dixon, having what appears to be the happy combination of greater firmness and fewer ties to city influentials with whom she would have to be firm, seems better positioned, as well as inclined, to do what is necessary. Mrs. Dixon also has been willing to talk about morality and ethical conduct in public service, a subject too many of the other candidates, in deference to the mayor or for fear of losing his voters (or, for a while, his endorsement) have scanted, saying mainly through some kind of shorthand only that they would be different. Mrs. Dixon says, rightly, that a community, even a large city such as this, lives by its values, and she is not ashamed to talk this way. We think it distinguishes her. It says to us, anyway, that she knows what is important and knows what are the right risks to take.

Of the others: Charlene Drew Jarvis, like Mr. Ray, has proven credentials as an effective and likable campaigner with strong working knowledge of all corners of the city as well as of the local legislative process. Like Mr. Ray, too, she has won impressively broad-based support. But for years Mrs. Jarvis countenanced problems on her staff involving committee business, campaign finances and political contacts that raised serious questions of propriety. This seems to us to bespeak a weakness.

It isn't fair to blame council members for all the problems of the city, as if they had been mayor. It is fair, however, to ask where they have stood in the past few years. Council member John Wilson has provided a model of sustained, detailed, cogent criticism of city budgets and of payroll bloat. As the city drifted into trouble, Mr. Ray and Mrs. Jarvis chose to be less critical.

After years of disagreeing with council chairman David Clarke on many issues affecting the city and on his priorities, we have found his campaign a pleasant surprise. Those differences remain, however, and his record of leading a fractious council doesn't argue for making him mayor.

Despite a lifetime of achievement as pastor and civil rights leader and elected official, Walter Fauntroy has run a campaign that has been a surprising low point. Mr. Fauntroy, a lifelong integrationist, incomprehensibly stooped to divisive racial politics. Too bad. He has also shown little knowledge of the structure of the local government or of ways to deal with its financial difficulties.

Can Mrs. Dixon win? The polls still say no. The situation is odd: more and more people who are turning out for candidate forums are saying that her message strikes the right note -- but that it's "too bad she can't win" or that maybe it's all just words. Still you keep hearing that what Mrs. Dixon is saying about returning local government to prouder days is sweet music, that the three council members and one House delegate all have been in office a long time and must share some responsibility for the state of city hall today. Those who come away from debates are praising Mrs. Dixon's intelligent responses and business-like approaches to questions about waste and inefficiency. They are discovering that Mrs. Dixon's roots in Washington are deep, that her understanding of, and concern about, the conditions that frustrate and alienate the poor are real. They are finding in Mrs. Dixon a woman whose business background, rise through the ranks to a very high place in the national Democratic Party and commitment to racial understanding are excellent qualities for a mayor to turn the national image of this city around to where it was -- and what it should have been all along.

One of Mrs. Dixon's friends of many years is Virginia Gov. L. Douglas Wilder, who knows more than a little something about come-from-behind campaigns run on relatively low budgets. "His basic counsel to me," Mrs. Dixon has said of Mr. Wilder, who has not endorsed anyone in the District campaign, included advice to "stay out there on the issues, go door to door, Metro stop to Metro stop." If the voters of the city do like what they hear from Mrs. Dixon, they can help answer the question of whether she can win -- by not second-guessing the outcome and on that basis voting for someone else. Sharon Pratt Dixon can win if enough people believe she should and vote to make it happen. Why not vote for someone who stands for real, large-scale change?