Classic theories of perception, cognition, judgment, and decision making assert that people exhibit diminishing sensitivity to magnitude changes. For instance, according to the value function of prospect theory (Kahneman & Tversky, 1979), the pleasure of moving from 0 to $1000 is larger than the pleasure of moving from $1000 to $2000, whereas the pleasure of moving from $1000 to $2000 is larger than the pleasure of moving from $2000 to $3000. In this article, I call into question how much diminishing sensitivity actually impacts choice and the nature of the value function. I advance a special form of diminishing sensitivity that I have termed rapidly diminishing sensitivity, which postulates that people are sensitive to the presence versus the absence of outcomes but are less sensitive to the scope of the outcomes when the latter differ from zero. Rapidly diminishing sensitivity yields a value function that flattens out rapidly as values move away from zero. In the special case where the value function flattens out immediately after zero, rapidly diminishing sensitivity assumes a discrete form that I have termed discrete sensitivity. I propose that rapidly diminishing sensitivity and discrete sensitivity are typically observed in experimental studies that involve extensive manipulations of the size of the outcomes across decisions, holding everything else constant. I provide evidence for my hypothesis in eight well-powered preregistered experiments across a wide range of domains, such as financial decisions, valuations of human lives, purchase decisions, judgments of goal-related performance, intertemporal choices, and moral decisions.