When choosing new Speakers, what matters most to you?

When auditioning new speakers have you ever listened to a pair you thought you really liked only to realize you didn’t like them at all after seeing their measurements/specifications? And I’m not talking about speakers that would be too difficult for your electronics to drive but rather, you just didn’t like their waterfall plot, or their frequency response or some other measurement even though subjectively, you loved the way they sounded? Conversely have you ever listened to a pair of speakers you did not care for only to change your mind after seeing their specs?
 

Assuming speakers can be easily driven by your home electronics, in other words, no compatibility issues related to sensitivity or impedance, what is the single most important thing you look for when finding speakers you’ll enjoy listening to? How do you go about confirming the speakers you buy will be enjoyable to listen to in your home system?