Housing and Urban Development Secretary Henry Cisneros said he will "stay and fight" rather than resign as an independent counsel begins to investigate whether he lied to the FBI during his pre-confirmation background check in early 1994. Cisneros announced his decision at a press conference soon after Attorney General Janet Reno recommended the appointment of the special prosecutor to probe allegations that Cisneros lied about payments to an ex-mistress. TIME White House correspondent James Carney says Cisneros, who had indicated his intention to resign if a counsel were appointed, apparently changed his mind after a long session with President Clinton, who is already weighed down with financial investigations of Commerce Secretary Ron Brown and Transportation Secretary Federico Pena. "Clinton feels strongly that Cisneros has been a good HUD secretary," says Carney. "And given all the problems that the president's been facing with his existing secretaries, the last thing he needs is another spot to fill in the Cabinet."