GOV. MARK SANFORD made a wise, if personally difficult, decision when he vetoed a 20 percent cap on property tax reassessments. The Legislature should make sustaining that veto one of its first orders of business when it returns to work next week.

But while this veto leaves a significant problem unresolved, lawmakers should resist the temptation to replace their own simplistic and problematic solution with the equally simplistic and problematic solution Mr. Sanford has suggested.

We were glad to see the governor call for “a more comprehensive debate of tax reform” and offer his willingness to explore any ideas legislators have to address the problem that escalating property values in popular neighborhoods cause for longtime homeowners. Unfortunately, the idea he singled out was eliminating reassessment altogether, and basing property taxes entirely on the purchase price.

This approach is attractive to politicians because it would produce some of the same benefits as a reassessment cap: It would put an end to those situations in which people who have no means of coming up with extra cash to cover huge tax increases — primarily retired and poor people — have to sell their homes; it would have much the same effect as an impact fee, by requiring new residents to shoulder more of the burden of expanded services and facilities; and, if it were structured correctly, it could save counties much of the $30 million they spend each year on reassessment.

More significantly, this approach would avoid the major problems the governor correctly identified with the 20 percent cap — that it is likely unconstitutional, and that it would distort an important school spending formula, resulting in a windfall from the state for some of the wealthiest school districts and a further reduction in funding for the poorest ones.

But doing away with reassessments would undermine the extremely sound idea that property — toward which local government services are geared — should be taxed based on its value. And it would do nothing to solve the big problem with an arbitrary cap that the governor didn’t mention: that it shifts the tax burden to people whose property values don’t increase that rapidly. When you lower property taxes for one group, you have to raise them for everybody else, unless you want to starve essential local services.

One reason property taxes are a growing problem is that the Legislature has already done its share of starving essential services — and local officials have taken the responsible step of trying to make up the shortfall. They’ve done that using the only substantial tool they have at their disposal — the property tax.

Property taxes wouldn’t be such a burden if the Legislature would fulfill its obligations rather than passing them off to local governments. Nor would they be such a burden if the Legislature would give local governments a wider menu of options for paying for schools and local services.

On the other hand, if the Legislature chooses to revive the arbitrary tax cap or eliminate reassessment altogether, property taxes won’t go down a penny. They’ll just be shifted to a different group of people — people who, understandably, will be banging on the State House doors in short order, demanding relief for the new tax burden that has just been placed on them.