IT IS NOT EASY to figure out from all the mixed statements and the backing and filling and the cloudiness hovering over the subject exactly what is going on concerning the proposed conversion of a part of the J. Edgar Hoover Building into a shopping arcade. But that may be the way the FBI wants it -- murky, your basic undercover public business. There have been endless statements and musings on the subject, however, in recent days and months on the these have only reinforced our own belief that the proposal is a good one. Many things have been said about this building, which houses the FBI and defaces Pennsylvania Avenue, but no one has ever said it is comely. One reason that the shopping arcade has merit is that it might humanize the physical presence of the building, which in fact looks like a cross between Lubyanka Prison and Reactor Number 2 at Three Mile Island.

J. Edgar Hoover, who gave his all to the bureau and his name to the infamous building, was -- when the subject first came up -- having none of it. Evidently while the building was being planned he vetoed all proposals for ground-level stores or anything else that might make the concrete complex more hospitable and accessible to the public. Legend has it that he feared such innovations would play hell with the bureau's security, attracting not just innocent strollers and shoppers, but also, well, frankly undesirable elements as well -- mugence Kelley, shared some of Mr. Hoover's misgivings. But Director William Webster has at least indicated that he is open to persuasion on the matter.

If Mr. Webster's own hesitations have anything to do with a feeling that it is somehow just not right for an august institution like the FBI to allow lowly commerce on its premises, it seems to us there is a simple solution. It would be no trick at all to set up shops in keeping with the basic functions of the FBI and in all respects congenial to Mr. Hoover's immortal spirit. For instance, you certainly wouldn't want a bank in the building, because if it were knocked over, that would be very embarrassing to the landlords, and might also result in some pretty nasty jurisdictional disputes. But there would be nothing unseemly about setting up one of those nice new boutiques, for instance -- something called "Edgar's," perhaps -- featuring a bold new line of men's aftershave called "Cointelpro." Or a bookstore, maybe called "Booked," that each week discounted the nation's 10 most wanted best-sellers. Or you could have one of those truly classy places like Neiman Marcus (G-Men Marcus"?) with a Christmas catalogue offering His and Hers mail covers.

If that's not enough to persuade Mr. Webster to go along, you have to ask yourself what will be. A chili joint named "Bonnie and Clyde's"? A kosher delicatessen featuring Dillinger Pickles? A dance hall