Don’t ordinarily hyphenate adjectival combinations of adverb + adjective or adverb + participle unless the adverb does not end in ly and can be misread as an adjective.

Now–if that sounds like just a bunch of silly grammarese to you, let us put it simply: Don’t hyphenate stuff like “fully involved” or “partially hidden treasure” — if you do, people in the know who read your ad, proposal, white paper, cover letter, or contract will move it to the bottom of the stack and give preference to your competitors who make fewer mistakes. That’s just a fact. Read on and find out if you’re making other similar mistakes.

Since the function of adverbs is to modify adjectives and verbs, and since participles are merely forms of verbs that can act as adjectives, the combination of adverb + adjective or adverb + participle is just a simple case of one word modifying another, and ordinarily no hyphen is needed to show the relationship.

An appropriately-red bridal gown and a completely-confused groom are errors in American English; there should be no hyphens. (The British often do hyphenate such compounds, however.) Some writers are misled by three-part compounds, such as a badly run-down neighborhood, and insert a superfluous hyphen after the adverb: a badly-run-down neighborhood. In this example there should be no hyphen between badly and run-down (which is correctly hyphenated as a participle + adverb adjectival combination).

Note that a scholarly-looking water skier is not an error. Scholarly, leisurely, and a few other adjectives end in ly, which is the standard ending for adverbs, but they are still adjectives, and the combination of adjective + participle, as in scholarly-looking, should be hyphenated.

Adverbs that do not end in ly and can be mistaken for adjectives
An ill-clothed baby is not an error, even though ill is an adverb and the combination is adverb + participle. The reason for the hyphen is that ill can be misread as an adjective, meaning sick and directly modifying baby rather than the participle clothed. The hyphen links ill to clothed.