High-stakes negotiations often go south when the parties perceive a lack of progress. Think trade-related brinksmanship, abandoned mergers, and athletes who walk away from failed contract extensions. In such situations, the absence of progress is decisive. For the same reason, though, the presence of small wins—tiny victories offering at least a glimmer of hope—can help avert disaster.

More immediately relevant to most of us, though, are negotiations that happen closer to home: negotiations, for example, with children who refuse to eat their darn food.

Here too, the lack of progress can lead to negotiation breakdown. And here too, the presence of small wins can make life negotiable. An anecdote to illustrate:

Suppose that I had two daughters and the younger of the two—let’s call her Penelope—was taking forever to eat her food and typically leaving most of it uneaten, day after day. Not that I do or she is. What would a despairing parent do?

Well, an increasingly insistent set of demands wouldn’t work: Penelope would just dig in her heels in the face of escalating parental frustration, trust me.

But what about creating some opportunities for small wins? What if Penelope, on a nightly basis, was actually failing to eat because she saw so little chance of finishing her entire meal and thereby getting the coveted cookie for dessert? Would small doses of dessert scattered throughout the meal serve as a stronger motivator than one big dose at the end?

And such I would decide to do with Penelope, if she was real and really resisting her meals. Specifically, I’d say that for every five bites of real food, she gets one small bite of the coveted cookie. And, lo and behold, it mostly worked…eh hem, would work.

Importantly, the strategy doesn’t involve any change in the reward structure—Penelope gets a whole cookie for a whole meal, regardless. So the strategy is less about upping the ante and more about instilling confidence in Penelope—specifically, the confidence that she can in fact make it to the next bite of cookie, seeing as it only lies three bites of pasta away, rather than a whole bowl.

Just as a president’s subtly positive statement can get a trade deal back on track, a subtly subdivided cookie can help avoid disaster at the dinner table—at least until the little negotiator requests the cookie after two rather than three more bites of pasta.