No, a Short Integer™ is not a Short Integer!

If an integer conforms to a special rule, I call it a Short Integer™.
Each integer can be tested. This is not a definitive list of Short Integers™.

Find the rule which determines whether or not an integer is called a Short Integer™.

_{Although it is a little inspired by the What is a Word™/Phrase™ series started by JLee, it is not exactly in the same spirit. In particular, there is no word-property tag.}