What is that order and logic?

Eon, two, ether, flour, verify, fixes, evens, weight, inner, net, leavened, wavelet, tethering, counterfeit, stiffener, existent, retentiveness, heightened, internecine, noteworthy. These 20 words are given in a definite, logical order. What is that order? What is the logic behind the words in the list? Is it possible to add further words to the list?

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The words are the shortest ones from which the names of the numbers, from ONE to TWENTY, can be spelled out. Numbers above TWENTY may be added to the list. For example, THRIFTY for THIRTY, FROSTY for FORTY, AFFECTIONATELY for FIFTY-ONE, and INTERCHANGE-ABILITY for both EIGHTY-NINE and NINETY-EIGHT.

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