You're mayor of a big city, and just when you need support for your controversial drive to land a baseball team, your town is rent by dicey issues of class, race and gentrification.

You a) head off on a taxpayer-paid trip to exotic China, b) announce plans for a soccer stadium in the city's most impoverished ward, c) choose this moment to close a shelter for homeless men and sell the building to an art museum, or d) all of the above.

If you chose d), you win the Tony Williams Political Acumen Award, bestowed upon those who master the art of undermining their own good intentions by looking right through the folks who pay their salaries.

Believe it or not, the city has decided to close the Randall Shelter for 160 homeless men and sell the building for $6.2 million to the Corcoran Museum of Art. The former junior high school on I Street SW will house the Corcoran art school and, temporarily, the museum offices while its 17th Street NW facility expands. Randall is just five blocks from the mayor's $440 million ballpark project.

The men at Randall can't quite believe that come Nov. 3, the doors will be padlocked.

"Southwest used to be a black part of the city," said William Jones, 54. "Now it's a place where I am no longer welcome. The mayor is setting it up so there's no projects in the center of the city. It'll all be for rich people. I pray every night that God intervenes and lets people see that just because people are homeless doesn't mean you can just push them out."

"It's insulting, man, insensitive," said Earven Thompson, 45, a recovering addict who is studying for a barber's license. "It's like they thought a bunch of pictures is worth more than me."

Advocates for the homeless argue that the mayor is systematically closing shelters to clear downtown of human refuse. Given the closing of Randall and the impending shutdown of the Franklin Shelter on 13th Street NW, "it looks like a pattern of moving people out of downtown and rapidly developing areas," said T.J. Sutcliffe, who runs So Others Might Eat. "You can close shelters, but people are still going to be downtown, for the same reasons other people go there: It's a convenient place to be."

But things aren't always as they seem: Catholic Charities -- which runs Randall and its replacement, a renovated building at St. Elizabeths Hospital in Southeast -- does not object to the closing because the new facility offers more space, privacy and services.

"It gives guys a sense of worth when you put them in a building that's warm and comfortable," said Charles McCrimmon, program director at Randall. "It's more conducive to them changing their minds and wanting to do something for themselves."

Randall, in contrast, is a leaky, dingy old school gymnasium lined with tightly packed rows of bunk beds. If one man snores like a Mack truck, 140 men spend the next day grumpy.

Changing locations is especially hard on men who are mentally disturbed. It will be difficult to persuade some to take a shuttle bus to St. E's, across the Anacostia River and three miles away.

Even those who understand the move don't want to go too far from downtown's meal programs and day work.

Lynn French, the mayor's senior adviser on homeless policy, said advocates should realize that subpar shelters are being replaced with better facilities -- albeit not downtown.

The District still plans to put a shelter in Southwest, "but we just aren't going to find sites downtown," she said. "There is no attempt to move the homeless out of downtown -- I wouldn't be a part of that -- but there is a premium on land downtown. We're spending millions to improve living conditions for the homeless, to help people reclaim their lives and get them back into their neighborhoods."

This mayor has increased beds for the homeless by more than 30 percent in the past two years. Yet all you hear is that he's pushing them out to make way for artists and the rich.

This mayor won back a baseball team that promises to boost D.C. coffers by shifting entertainment spending from affluent suburbs to the hard-up city. Again, the perception is that the stadium is for the rich.

Few politicians could match this mayor's mix of concrete success and abstract failure. Not many try. The mayor's hosts in Beijing never have to worry about how their policies are perceived. Maybe that's why Williams had such a fine time there.