The following thirteen words have a special property common to all of them (though they're not the only words with this property):
SADIST, THOROUGHFARE, HYMN, POISED, YURT, THIRTY-SEVEN, STREWN, VERTICALITY, INERTIA, BALDERDASH, HIGHFLYING, REWARDING, OPINIONATED
Firstly, what is this property? Secondly, which two words in the list have the property more than the other eleven?
Hint:
the idea behind this puzzle also appears in another puzzle posted in the last few days, although that one is less enigmatic.