Every year around this time, people grumble about their tax bills. This year, taxpayers who lost the deduction for state and local taxes in the 2017 tax overhaul bill — mainly those in California and states in the Northeast — are going to grumble even more. And for some, that grousing has turned to talk of fleeing to lower-tax states.

Those wealthy enough to own homes in multiple states will want to have their cake and eat it, too. Some will try to establish residency in one of the seven states that have no state income tax: Alaska, Florida, Nevada, South Dakota, Texas, Washington and Wyoming.

In doing so, they will reduce their tax bills substantially: up to 13 percentage points for California residents, for instance, or nearly nine points for those in New York and New Jersey.

The people trying to take advantage of this strategy have always been a target of state tax collectors, but financial advisers say states like California and New York have stepped up their collection efforts, and they urge caution for anyone considering this approach.