T most corporations, new rules to ensure that a majority of directors are independent and serving shareholders' interests are finally in effect. But just how assiduously are they being followed?

The short answer is, not as much as shareholders may have hoped. The way the New York Stock Exchange and the Nasdaq market wrote their rules, it is pretty much up to a company's board to judge whether a director is truly independent. And some boards - the one at Computer Associates, for example - appear to be taking liberties.

Both exchanges now require companies whose shares they trade to have boards with a majority of independent directors. In addition, audit committees and compensation committees must be made up entirely of independent directors. And Securities and Exchange Commission rules call for at least one member of a board's audit committee to be knowledgeable in accounting and financial reporting.

The exchanges even give boards some clear-cut tests. For example, someone who receives $100,000 or more a year in compensation that is not related to directors' fees, pension or deferred compensation is not considered independent by the Big Board. The Nasdaq draws the line at $60,000.

But the rules also note, correctly, that it is impossible to anticipate all the situations that may compromise a board member's independence. Therefore, according to the Big Board's rules, "it is best that boards making independence determinations broadly consider all relevant facts and circumstances.'' The exchange goes on to say that each board should consider the issue not only from a director's point of view, but also from that of the people or organizations with which he has an affiliation.

In other words, relationships matter.

The regulations, of course, were a response to downright chummy boards at Enron, WorldCom, Tyco and other companies that let executives do as they pleased with shareholders' money. Most American companies must comply with the new rules by Oct. 31.

Read any recent proxy statement and you will see how a company is responding to the requirements. The filings usually say flatly that the board has determined that a majority of directors meet independence standards.

NOT so fast, says Donn Vickrey, a founder of Camelback Research in Scottsdale, Ariz. He says some of the companies' claims of independence are dubious. And the disclosure of directors' relationships with management, he said, leaves much to be desired.

"There is definitely a noticeable improvement in independence among board members," Mr. Vickrey said. "But there are also a significant number of firms who are clearly making things sound better than they really are.''

Mr. Vickrey and his colleagues conduct extensive background checks on directors, looking for relationships with management that could impair their independence.

He sees the Select Medical Corporation, a health care concern, as Exhibit A. Select Medical, based in Mechanicsburg, Pa., is traded on the Big Board. In his view, longstanding relationships between management and certain members of the company's board call into question its claims that directors are independent.

Consider this: Select Medical's founder and chief executive is Rocco A. Ortenzio. Russell L. Carson, a director who is on the compensation committee, is co-founder of a private investment firm, Welsh, Carson, Anderson & Stowe, that focuses on health care concerns. According to a proxy statement of U.S. Oncology, on whose board both Mr. Carson and Mr. Ortenzio have served, Mr. Ortenzio often invests with Welsh, Carson.

The web gets even stickier. Leopold Swergold, who serves on Select Medical's audit committee, founded Swergold, Chefitz & Company, a health care investment firm. But Mr. Swergold has been a director of Rehab Hospital Services, a company founded by Mr. Ortenzio in 1979 that was sold in the mid-1980's. More recently, Mr. Swergold has been an advisory partner in Select Capital Ventures, a health care investing company founded by Mr. Ortenzio. Neither of these associations is mentioned in this year's Select Medical proxy.

"There's no doubt that most of the board members have friendships and relationships over time,'' said Michael E. Tarvin, general counsel at Select Medical. "I think it's pretty clear that the N.Y.S.E. and any governing authority that would make rules would have to avoid any standard that would focus on friendship or relationships.'' And the friendship between Mr. Carson and Mr. Ortenzio is no secret. "They have known each other for some years, consider each other friends and Welsh, Carson has provided some financial backing to another company started by Mr. Ortenzio,'' Mr. Tarvin said. "Based on their current relationships, interlapping board service and other factors, I think the conclusion is they are friends but Russell Carson would act independently.''

He added that Mr. Swergold's affiliations with other Ortenzio ventures created no independence problems.

Select Medical's board affirms in its proxy that its audit committee members have the required financial or accounting expertise, and calls them "financially literate.'' But then comes this unusual disclaimer from the audit committee: "We are not accountants or auditors by profession or experts in the field of accounting or auditing,'' the proxy notes. "Furthermore, our considerations and discussions with management and the independent auditors do not assure that the company's financial statements are presented in accordance with generally accepted accounting principles, that the audit of our company's financial statements has been carried out in accordance with generally accepted auditing standards or that our company's independent accountants are in fact 'independent.' ''

Mr. Tarvin said that the remarks were "intended to state that although these persons are financial experts, they have not conducted an audit.''

Another standout on director independence is Computer Associates, the software company that has been plagued by accounting irregularities. Its shares also trade on the New York Stock Exchange; the company, based in Islandia, N.Y., held its annual meeting of shareholders last week.

Computer Associates' board, led by Lewis S. Ranieri, a former Salomon Brothers vice chairman, says the chairman of its audit committee, Walter P. Schuetze, is independent. But this view can certainly be questioned, given that, according to the proxy, the company paid $125,000 in "additional director fees'' for "his extraordinary services in connection with the audit committee investigation concerning the company's prior revenue recognition practices.'' None of the other audit committee members received additional payment for the investigation.

Mr. Schuetze, a partner at KPMG for more than 20 years who then became chief accountant to the division of enforcement at the S.E.C. from 1997 to 2000, certainly has the necessary accounting expertise to run the audit committee at the company. And because of the company's aggressive accounting in the past, he may have had to do some heavy lifting.

Before joining the Computer Associates board in 2002, Mr. Schuetze served as a consultant to the company on financial matters; he received $100,584 in fees and expenses in fiscal 2002.

Last summer, with prosecutors investigating Computer Associates' accounting practices, the company authorized the audit committee of its board to conduct an "independent investigation'' into the company's activities relating to recognition of software sales. The committee, led by Mr. Schuetze, found that sales were recognized prematurely in 2000. Four executives resigned; three pleaded guilty to securities fraud charges.

Last April, Computer Associates restated its results for fiscal 2000 and 2001. Two months later, Sanjay Kumar, its chief executive, resigned.

Mr. Ranieri said in a statement on Friday that "any claim that Walter Schuetze's role in heading C.A.'s audit committee investigation was anything but independent is misguided.''

The statement went on to say that "the additional director fee paid to Walter was consistent with the highest standard of corporate governance including the requirements of Sarbanes-Oxley and related S.E.C. and N.Y.S.E. rules." As a director fee, the statement continued, it was in compliance with all legal requirements and was approved by the company's inside and outside counsel.

In an interview on Friday, Mr. Schuetze declined to comment.

Typically, when there is an internal investigation, a board hires independent experts to conduct it. Since Mr. Schuetze led the one at Computer Associates, he then, as chairman of the audit committee, had to review the adequacy of his own inquiry. That presents a potentially glaring conflict.

Gary Lutin, an investment banker at Lutin & Company who is conducting a forum for Computer Associates shareholders, said: "Based on the information C.A. has provided so far, all we know is this: that directors who are being sued, personally, decided to give one of their colleagues a $125,000 bonus for heading up an investigation of the evidence against them, and that they decided to call their colleague independent. This is not a foundation for confidence.''

OF course, the New York Stock Exchange could weigh in on whether the directors of Select Medical or Mr. Schuetze at Computer Associates are indeed independent. Under the exchange's rules, it can issue a public reprimand letter if a company fails to comply. Janice O'Neill, vice president of corporate compliance at the Big Board, says the staff is scrutinizing proxy materials and supporting documents related to director independence for every listed company. No violations have been identified yet, she said.

Investors, meanwhile, are left to wonder if the independence that they need from their directors is the independence they are getting.