That both Zoe Baird and Kimba Wood were done in by their hiring of illegal aliens is a bizarre coincidence. But more is involved than either bad luck or a common yuppie transgression striking twice in the same place. In fact, the extraordinary role of Hillary Clinton has distorted the process.

President Clinton followed the Baird embarrassment by picking U.S. District Judge Wood, a woman who, like Baird, boasts modest legal credentials and is a stranger to him. Surprisingly, the First Lady interviewed Wood for 90 minutes, twice as much time as the president spent with his prospective chief legal officer, according to White House sources.

The anti-nepotism law inspired by Robert F. Kennedy's tenure at the Justice Department prevents the president's wife from being a de jure attorney general, but she shows every inclination to do the job de facto, with somebody else as figurehead.

Indeed, difficulties in filling the last Cabinet slot were not just caused by the arbitrary requirement that the attorney general be a woman. The bigger problem, in the view of one prospective candidate for attorney general, is that the nominee must agree in advance to pre-selected subordinates picked by the First Lady.

That -- and not worries about her federal pension -- may be the real reason Clinton's first choice, Judge Patricia Wald, turned down the job. Word among staffers at the U.S. Courthouse here, where she works, is that she refused to rubber-stamp Clinton's choices for deputy attorney general, associate attorney general and solicitor general.

The proposed deputy is the well-respected Charles Ruff, the last Watergate special prosecutor, whose credentials dwarf those of the two women selected to be his boss (but who now has run into trouble over his housekeeper's Social Security taxes). The associate AG, who would run day-to-day business at Justice, has the clear Hillary Clinton imprint: Webster Hubbell, her former partner at the powerhouse Rose law-lobbying firm in Little Rock.

Solicitor general, the job second only to attorney general in prestige, will reflect Mrs. Clinton's wishes when finally filled. Well-placed Democrats believe she wants the brilliant, very liberal Georgetown law professor Peter Edelman, husband of Marian Wright Edelman, the first lady's friend and godmother of the Clinton administration's left wing. If the president decides diversity requires a black, the nod could go to Yale Law Professor Drew Days, a former assistant attorney general.

Trouble finding a woman to sign on as nominal boss of this formidable crew was why Clinton rushed the selection of the Aetna insurance company's general counsel to meet his Christmas Cabinet deadline. After Baird went down, the White House contacted the esteemed U.S. District Judge Rya Zobel in Boston, but she came over as a woman unwilling to be anybody's figurehead, according to federal judiciary sources.

So the answer was Kimba Wood, 49, described by friends as highly intelligent but private person unsuited to big-time politics. Quite apart from her baby-sitter problem, she was unfamiliar with criminal law and lacked any courtroom lawyer experience before being named to the bench in 1988.

Wood might have been lost in judicial obscurity and never considered for attorney general had she not captured the headlines on Nov. 28, 1990, with an unduly harsh 10-year sentence for financier Michael Milken (which she later reduced to two years). Bolstering that was her friendship with Susan Thomases, a Hillary Clinton confidante who works hard to keep Bill Clinton on the left.

His second failed choice hands Bill Clinton an opportunity. He can start from scratch and find a qualified lawyer, woman or man, who would really be in charge. But that would mean telling Hillary Clinton she will not be in control at Justice.