Ms. Courts plans to invite Mr. Welker over for dinner at her house, so her four sons can get to know him. ''It really makes people human you admire from afar,'' she said.  In turn, Mr. Welker plans to give Ms. Courts backstage tours, cook her dinner and send her birthday gifts. He said he would never refuse an invitation from her. ''She is really a cornerstone of this community,'' he said. ''I would definitely rotate my schedule to accommodate anything.''  He added, ''To be quite frank, they are paying your salary.''  The sponsorship, he said, does bring pressure -- but only to become a better artist. ''In a way, she's investing in a product,'' he said. ''And you're that product.''  IT'S just that kind of unabashedly pecuniary logic that has caused three of the country's large ballet companies -- New York City Ballet, Houston Ballet and San Francisco Ballet -- to decide against the sponsorship of individual dancers. The purists argue that dancers should spend their time dancing, not worrying about where their salary is coming from or kowtowing to their sponsor. Ballet companies impose strict artistic rankings on their dancers, and some fear that allowing donors to single out individuals will undermine that system, either by creating an alternative measure of a dancer's worth or by allowing donations to influence casting.  ''It starts to get into areas that should be at the sole discretion of the artistic management,'' said Christopher Ramsey, the director of external affairs at City Ballet. ''People might have an honest difference of opinion. It's best if you can avoid those, especially with people who are trying to help you.'' He added: ''You're opening a door where funding is contingent on individuals performing certain roles.''  City Ballet sees itself as an ensemble company, to such an extent that it refuses to reveal casting decisions before a show. ''The idea has always been that we are presenting art, and you come on a given night to see art,'' Mr. Ramsey said. As such, he continued, ''we attempt to gain support for our more general endeavor.''  On a more practical level, some worry that donors might bolt when their chosen dancer moves to another company or retires. ''Dancers come and go,'' said Thomas W. Flynn, the director of development at San Francisco Ballet. ''We want people to support the ballet as an institution, rather than supporting an individual artist.'' At Atlanta Ballet, one couple was interested in sponsoring Stacey Slichter, a gregarious and popular dancer. But next year Ms. Slichter will be teaching, not dancing, and so far the company hasn't been able to align the donors with another dancer.  To counteract an excessive emphasis on individual dancers, some companies, including Atlanta Ballet and Ballet Theater, route all sponsorship donations to their general funds. ''The money doesn't go to pay that dancer's salary,'' said Rachel S. Moore, Ballet Theater's executive director. ''That's not what this is about. It's about supporting the company.''  Houston Ballet took an even more conservative tack. It offers donors the opportunity to endow a dancer position, in the manner of an endowed chair at a symphony or university, rather than to sponsor an individual artist. It costs $500,000 to endow a principal dancer position; income from that capital is used to pay half the dancer's salary. When the dancer leaves, the endowment stays. Pacific Northwest Ballet, Pittsburgh Ballet Theater and Pennsylvania Ballet, among others, have similar programs.  Another concern is that individual sponsorship -- along with the extracurricular attentions of a wealthy, powerful patron -- could stoke the already intense competition among dancers. At Houston Ballet, endowed positions are typically filled by seniority. ''That way it doesn't become some kind of popularity contest with an individual donor,'' said Cecil C. Conner Jr., the company's managing director. At Ballet Theater, the dancers participated, but requested that management find sponsors for all principals within a year. Luckily, donors cooperated, and every dancer found a match. ''You don't want any dissension, or people feeling unwanted,'' Mr. Stiefel said. ''Dancers are artists. We are sensitive people.''  At Ballet Theater, which is better known for its individual stars than for its ensemble work, sponsorships have pulled in about $1.2 million so far this year, just over 6 percent of estimated nonendowment fund-raising. Not everyone has been so successful. No dancers at Pacific Northwest Ballet have sponsors yet; prices range from $25,000 for a corps dancer to $100,000 for a principal. At Pennsylvania Ballet, 2 out of 22 eligible corps dancers have sponsors, and at the Joffrey, 3 of 8 apprentices have been picked up. Since Atlanta Ballet's program was founded last February, only 2 of the company's 23 dancers have been chosen. John Clark, the director of development, said the unsponsored dancers joke about the disparity, as in: ''Well, you're sponsored, so you must be special.'' But he said that the teasing was light: ''They're joking that they are hurt, but they aren't. It's a big family.''  Indeed, the ballet world's most pressing fears about dancer sponsorship have so far failed to come to fruition. Even a recent case in which a patron was allowed to actually hire a company's dancers turned out just fine. Three years ago, Dennis Law, a retired surgeon who is a board member of Colorado Ballet, went to China, his birthplace, and scouted for dancers. He found two he liked and offered to pay their living expenses and salaries for a year. Martin Fredmann, the artistic director of Colorado Ballet, promptly hired them, without ever having met them.  ''I did something I rarely do,'' Mr. Fredmann said. ''I accepted them from videotape.''  Mr. Fredmann does not feel his artistic vision was compromised. ''The situation was: these dancers come, if they don't work out, they don't work out,'' he said. ''There was nothing that said that I had to do anything. I was in complete control of the situation.''  It turned out that Kang Hua, the young woman Mr. Law had selected, was too tall for the company. She languished in the corps, and after one year returned to China. But Mr. Law's other pick, Zhuang Hua, went on to principal roles and stayed with the company for three years, until he was hired away by Ballet West, based in Salt Lake City.  ''Of course, people were wondering what kind of dancers they were and how they look and whether they would be favored for casting,'' said Sharon Wehner, a principal with Colorado Ballet. ''But what happened is the dancers just basically had the same kind of opportunity that everybody else had -- which is the opportunity to succeed or fail.''  Mr. Zhuang's story has the ring of a happy capitalist fable. He had never been to America before Mr. Law arranged his passage. He now speaks English, owns a car and most important to him, he says, his dancing has improved. ''When I'm ready,'' he said, ''I can go back to my Chinese company and teach them what I got here.''
American ballet companies have recently begun allowing donors to sponsor individual dancers, for amounts range from $2,500 to $100,000 a year; some ballet companies even compile and distribute rosters, which look eerily like shopping lists, specifying their dancers' ranks and prices; new initiative has generated good deal of controversy; in process, it has raised awkward questions about how far companies will go to generate revenue; about relative popularity of various dancers, and about what exactly patrons are buying; some sponsors and dancers they sponsor comment; photos (M)