One of the things I learned in high school German class was never, ever to accept a compliment. The proper response is denial; graciously accepting someone's praise in Germany is hopelessly gauche.
Fortunately, a similar aesthetic regarding compliments prevails in Japan, as this Japan Times article suggests. So even my first time in Japan, around 1998, I was habitually denying the overwrought compliments offered on my truly atrocious Japanese. Anyone I know whose Japanese skills are actually worthy of praise ceases directly hearing even a word of such, unless they are particularly tired and sloppy and making mistakes. Such people are offered praise (or bewilderment) through intermediaries.
Unlike Germany, however, it seems to be far more common for Japanese to lavish praise on people, so the skills in deflecting compliments require somewhat faster reflexes.
It is somewhat news to me, though, that I would need to be cautious about group contexts when offering compliments to people close to me... But since Americans can be insulted by insincere compliments, I suppose the same risk would be present in U.S. situations; offering an insincere compliment to someone you know in a mixed group might be taken particularly badly. I think that the most sincere direct compliment in Japan is when someone is saying that they like something about you (I like your hair when it is longer) or something that you have done (is it ok if I eat more of this?), rather than offering general praise (your Japanese is good, etc.)