It’s quite a crowd that is gathering today and tomorrow at Washington’s Mandarin Oriental Hotel for the annual spring meeting of the Council of Institutional Investors. Vice President Gore is scheduled to give a speech, as is the new chairman of the House Financial Services Committee, Barney Frank. The California state treasurer, Bill Lockyer, is expected to attend, as is Stephen Schwarzman of the Blackstone Group, who, the Wall Street Journal reported over the weekend, stands to double his personal wealth of $10 billion by taking Blackstone public.

These institutional investors have brought a lot of pressure to bear on American companies in recent years, some of it for the best. But at their worst, the institutional investors — particularly the big public pension funds — have come to resemble the very corporations whose practices they are so fond of deploring. The institutional investors, for example, make a fuss about the practice of boards employing compensation consultants who may be biased because of fees they earn from work for company management.

Yet many public pension fund boards employ their own investment consultants who earn fees not only from the fund boards but also from the money managers they are advising the pension funds to put money with. To cite just one example, Callan Associates, a firm that advises both the New York City Employees’ Retirement System and the Connecticut state pension fund, says it gets at least 30% of its revenue from money managers, the same money managers about whom it is advising the pension funds on investing.

Another conflict that the public pension funds are prone to is hiring lawyers and money managers who give campaign contributions to the elected officials who serve on the pension fund boards. It’s hard to avoid the appearance of pay-to-play. Many of those class-action lawyers will be roaming the hallways of the Mandarin Oriental today and tomorrow, rubbing elbows with the pension board trustees they hope to represent in shareholder lawsuits. One Massachusetts lawyer, Jeffrey Block, who donated to the campaign of the New York City comptroller, William Thompson Jr., told us that he made the contribution after hearing Mr. Thompson speak at a meeting of the Council of Institutional Investors.

Mr. Block’s firm, Berman DeValerio Pease Tabacco Burt & Pucillo, is among those that represent the city pension fund, on whose board Mr. Thompson serves as a trustee. The complaint of the corporate governance crowd is that corporate America has gotten too fat and cozy and complacent. The institutional investors are trying to keep the corporations on their toes, but sooner or later more people are going to start wondering who is keeping the institutional investors on theirs?