If you think finding an apartment is hard, try finding nearly 500 of them. That’s what city Human Resources Administration Commissioner Jason Turner has to do by June 30 to make sure he’s not held in contempt of court.

At a hearing on Friday in the years-long legal battle to keep kids and their parents from sleeping on the floor of the Emergency Assistance Unit office and from shuttling from temporary shelter to shelter, city lawyers pleaded with State Supreme Court Judge Helen Freeman that the city was working as hard as it could to recruit landlords willing to house homeless families, without success. Last October, HRA promised to create a new program to help move hundreds of homeless families to permanent private housing. But as of mid April, the agency reported placing just 11 families.

Their reason is obvious, said Legal Aid Society attorney Steve Banks, who presented the contempt-of-court motion: “The program has been conceived at a level that is ineffective.” For a two-year term, it offers landlords just $550 a month for a one-bedroom and $800 for a four-bedroom–about a third less than what landlords get under federal Section 8 subsidies. At the hearing, city attorney Leonard Koerner asserted that the payments are being kept low deliberately, to make sure tenants aren’t socked with unaffordable rents when the subsidies expire.

Since Legal Aid filed its contempt motion against Turner and Mayor Giuliani on April 11, city officials say, no families have been sleeping on the floor. According to Legal Aid, however, at least 1,600 families were shunted to temporary shelters in the last month, 238 for a week or more.

Judge Freeman delayed a decision to give the city more time to find apartments. But HRA is having trouble even when it can offer landlords more money under other programs. It has access to Section 8 vouchers, but “we have not been able to use them the way we thought we could,” Chief Assistant Corporation Counsel Leonard Koerner told the court.

Landlords get cash bonuses for each lease-signing. Section 8, however, is notoriously annoying. Buildings must be immaculately maintained, and the city is reportedly slow to perform pre-rental inspections, forcing owners to keep apartments vacant for weeks. The city and Legal Aid will be meeting with the Rent Stabilization Association to see how it can persuade its member landlords to rent to homeless families.

Shelter operators–who likewise get bonuses for finding apartments for clients–say incentives are putting money in the wrong place, too late. “The one thing the administration has not done well is the creation of additional housing,” said Frederick Shack, president of the Tier II Coalition of family shelter providers. City investment in affordable housing development has declined 44 percent since 1994. “If I’m looking for a unit that doesn’t exist, all the incentive in the world isn’t going to make it appear.”