Asking for a raise is one of the most fraught parts of a working life, a process maniacally Googled and agonized over with friends. Advice is often conflicting. Don’t give your number first, or always do. Start with a number you don’t really expect to get, or ask for nothing at all.

A frequent piece of advice, enshrined in one of the standard business school texts (pdf) on negotiation, is to avoid giving a salary range, because an opponent or manager will seize on the low end.

Not only is that advice dead wrong, but done right a range actually leads to better results than going with one number, according to a new study from researchers at Columbia University, first covered at The Wall Street Journal (paywall).

It’s not that people don’t know to throw out a range. More than half of people reported using one at some point in their most recent negotiation, a separate study (pdf) recently found. But there’s scant advice on how to figure out the correct range to use, or at what point in the negotiation to deploy it.

The Columbia researchers had a hunch, and their study bore it out, that a specific “bolstering range” can actually be very effective. It means setting a fairly ambitious number at the bottom range, equivalent to the one you would have used as a single point offer, and then a higher number as the top range.

It refutes conventional wisdom that says people have selective attention, that they focus exclusively and narrowly on the number most attractive to them. In fact, the authors show that people are a bit more complicated than that.

First, a range shapes expectations about an acceptable counteroffer. When there’s a number explicitly framed as a floor, people assume you’re unlikely to take something below it. They don’t necessarily make the same assumption with a single number.

Second, there’s the politeness effect. People are much less likely to go way below the bottom number of a range because they feel like it would be insulting. Similar qualms aren’t nearly as strong with single-point offers. And offering a range is generally seen as a sign of flexibility, even when the actual numbers are relatively high.

The researchers conducted a series of five experiments. In each case, a bolstering range led to better counteroffers, higher estimates of the lowest price someone would take, and a resolution—whereas starting with a single extremely high number had the negative effect of simply shutting down more negotiations or having them end in an impasse.

They also found that a bracketing range, where you put a floor below the number you really want and a ceiling above, doesn’t work nearly as well.

An experiment pitting two people negotiating over the sale of a used car found that a bolstering range led to an average counteroffer nearly $200 dollars higher than a single-point offer, and a higher-end settlement ($6,985 versus $6,776). Bolstering ranges also outperformed bracket ranges and extremely high, single-point offers.

But the bigger payday isn’t the only benefit of offering a bolstering range. People sometimes forget that it’s not all about money, that the relationship with a superior afterwards matters as well.

Across the experiments, people offering the higher range weren’t seen as any more aggressive or obnoxious than those who offered a single point, even though the high end of their range was a much larger amount. They were also seen as more flexible and confident.

So if you’re not making the first offer in a negotiation, consider doing so (the research on how that anchors negotiations is well established), and once you do, make it a bolstering range.