Only a single homeless person has taken up the Government's cash offer to leave Auckland, but Paula Bennett says she's "thrilled, honestly" with the month-old scheme.
The Social Housing Minister rushed out the policy ahead of May's Budget, to the surprise of Finance Minister Bill English.
Since going live, 12 families have fled the increasingly unaffordable city, taking $54,508 with them.
Half of them have moved into private accommodation, so that money's likely gone to landlords. Only one person was homeless, and four were staying in emergency temporary accommodation.
When asked by Paul Henry if the figures were disappointing, she said no.
"I'm honestly not [disappointed]. We did need to take it carefully, make sure they're going to the right places, making sure they've got the support."
"I'm thrilled, honestly."
Ms Bennett then adopted a faux-pompous voice to mock her critics.
"In one respect I get this, 'It's rushed and you're just kicking people out and you're rushing them.' And now I'm getting, 'It's too slow - why aren't you kicking more people out?'.
She said one Auckland woman who moved to Hamilton was now able to apply for jobs, "which she couldn't do in Auckland because of transport".
Labour deputy leader Annette King, appearing on the show with Ms Bennett, said the $5000 policy was "well on the way to being a failure".
"The idea that you could get $5000 and move, I think [Ms Bennett] thought a lot more would be attracted to it."
Ms King joked that after leaving Auckland, they could get given another $3000 to move back under a Government plan to get people into work.
"I don't think Annette understands the policy," replied Ms Bennett.
The Government set aside $750,000 for the policy.
It's estimated tens of thousands of New Zealanders are homeless.