Wu, Sheppard, and Mitchell (Br. J. Psychol., 2016; 107, 1-22) found that observers could accurately identify people with extreme but not more average empathy scores. Here, we further consider this U-shaped discrimination function. We first examine a statistical issue regarding the construction of the average groups, which are less homogenous by definition than the extreme groups. We then consider the kinds of questions arising when these results are considered within the adaptive framework of signal theory. Some interesting questions arise relating to the signal sender, including the costs and benefits to the sender in revealing and concealing true empathy levels, and the effects of adopting behavioural norms to conceal true levels of empathy.