HELP WANTED: Chief executive of the Smithsonian who won’t use its funds to clean his chandelier, heat his pool, install French doors or pay his chauffeur; who will take fewer than 70 vacation days a year; who won’t keep crucial information from the general counsel, inspector general and chief financial officer; and who won’t decorate his office with a stuffed Bengal tiger from the Natural History Museum.

If the Smithsonian Institution knows what it does not want in its next secretary, it seems less sure of the kind of leader it should be seeking, particularly now that the job description is changing.

Should it be an experienced arts manager, comfortable balancing the interests of museum directors, donors and boards? A business executive steeped in management? Or perhaps a university president adept at dealing with influential alumni, educators and government officials?

The opening at the Smithsonian is a result of the rocky tenure of Larry M. Small, former president and chief operating officer of Fannie Mae, who resigned in March after disclosures about lavish spending. Two lacerating reports — one internal, another from an outside review committee — describe a chief executive run amok, devoting much of his time to corporate boards.