This spring, the City Council celebrated new help for homeless New Yorkers: a generous boost in dollar value for city-issued rent vouchers so stingy many recipients can’t find apartments cheap enough to use the aid.

Now, formerly homeless people are looking at the fine print and learning to their dismay that the new, more generous CityFHEPS program could lock them out of their apartments and send them back to shelters.

The new vouchers will be pegged to the federal Section 8 program, which guarantees tenants pay no more than 30% of their incomes toward rent. The program currently allows rent of up to $2,053 for a two-bedroom apartment, with the government paying the difference.

But one CityFHEPS feature hasn’t changed: once enrolled, participants can earn no more than 250% of the federal poverty level, roughly the city’s $15 minimum wage for a full-time worker. And they must recertify their income every year.

This so-called income cliff forces voucher users who get offered a better-paying job or a raise to leave the program entirely, even if their rent is still unaffordable.

And to initially get into the program, someone can make no more than twice the poverty level, meaning a full-time minimum wage worker cannot qualify at all.