What in the world is a compound modifier?

When two words act as one to modify a noun, they become a compound modifier.  For example: 

The deep-draft vessel went aground in the harbor.

As used here, neither deep nor draft could stand alone to describe vessel, so the term is hyphenated to indicate that they used as a single unit, or a compound modifier.

Sometimes, however, a compound modifier should not be hyphenated.  When the modifying term contains an adverb ending in “ly,” there is no need to add a hyphen because the “ly” lets the reader know that it is part of a word pair modifying a noun. 

See the explanation from section 7.86 of The Chicago Manual of Style:

Compounds formed by an adverb ending in -ly plus an adjective or participle (such as largely irrelevant or smartly dressed) are not hyphenated either before or after a noun, since ambiguity is virtually impossible.  (The -ly ending with adverbs signals to the reader that the next word will be another modifier, not a noun.)