My Websters II has this usage note:

When functioning as an adjective, a form such as encouraged or pleased may be modified by very alone (a very tired child); a very interested audience). When a term functions as a past participle in a verb phrase, the appropriate modifier is very much (has been very much praised by the critics; was very much enlightened by your explanation). Thre are many borderline cases, however, where either modifier may occur, as in was very (much) mistaken.; was very (much) distressed.

Now this doesn't really answer the question, but I'm a pretty good writer and I would not interchange very and completely only for the reason that very satisfied and completely satisfied are not the same thing. Completely is an absolute. Very is comparitive. Very happy leaves room for improvement on the level of happinenss.

TEd



TEd