What is a Tower Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.

If a word conforms to a special rule, I call it a Tower Word™.

Use the following examples below to find the rule.

And, if you want to analyze, here is a CSV version:

Tower Words™,Not Tower Words™
ANVIL,HAMMER
AX,SWORD
COOCOO,RAVEN
DRUG,COCAINE
FILET,BEEF
HUG,KISS
KUSSOS,WHAT
PI,MATH
TILT,SLANT
US,ME
VILE,GOOD
WHY,NOT
XU,CHINA
ZEE,EASY

• Hey, nice Homestuck avatar! :D – Deusovi Sep 15 '16 at 3:07
• @Deusovi Agreed :P – Arcturus Sep 15 '16 at 3:24