Now, authors of a just-published study say a hard-line approach forcing pet cats to be confined for 24 hours would have the biggest benefit for wildlife.
But of all the potential measures on the table, this was the one most unlikely to win the support of owners.
Victoria University's Professor Wayne Linklater and colleagues surveyed customers at vet clinics, along with 173 veterinarians themselves, over four weeks.
They asked about several potential steps – desexing, limiting the number of cats per household, microchipping and having them inside or contained all night – and found their appeal fell in just that order.
Registering cats, as was the practice for dogs, or putting a collar on them, were actions less likely to be adopted.
But disagreement was strongest when it came to the suggestion that cats should be kept inside properties at all times.
Nearly all owners who took part in the surveys – carried out across Wellington, Dunedin and Palmerston North – had desexed their cats and nearly two thirds had microchipped them.
Just over a quarter of respondents locked their pet inside at night every night and a similar number collared their cats.
Linklater said the aim of the study, which drew on a technique used in public health interventions, was to be considerate of owners' beliefs and values, rather than be "antagonistic" toward them.
"We are really trying to find the one thing that is the path of least resistance through all of the controversy and conflict."
Linklater believed more of this participatory research with owners could help resolve the problem.
"It's about acknowledging from the outset that cat owners are going to have to be part of the solution, so it's best to engage with them early on so that the strategies you design are informed by them," he said.
"At the moment, there are really two approaches to this problem – one is the top-down approach where you make rules and try to force a change, and the other, of course, is to work from the bottom up with communities.
"The top-down approach is already happening to some degree, and it's effective in some places, but of course, it risks non-compliance and non-co-operation.
"So what we've developed is a strategy that complements the bottom-up approach, and the next step is to use this information to design a campaign that works with pet owners on ways that reduces their cats' ability to hunt."
Many towns and cities across Australia had introduced cat curfews over recent years, he said, and such a step could be the first in a long-term movement here.
Forest and Bird chief conservation manager Kevin Hackwell questioned whether that was the right approach.
"Yes, we want to people to be self-managing and doing the right thing, but having a set of rules and boundaries helps manage things for the majority - and you therefore get overall benefits for everybody."