The alt attribute can actually be much longer than 3 words. They say
that a picture is worth a thousand words, but I wouldn't quite go that
far :).  At any rate, more than three words is certainly fine. Make it
a simple description without going too far to describe alternatives of
alternatives.

For instance, in the example I mentioned above, using "puppie playing
with ball, dog playing with toy, small dog, pet toy, play ball, cute
puppie, betsie puppie with ball, cheap dog toys, pet toys, animal
food, animal care, pet care, puppie care, puppie toys" would be going
a bit tooo far (not to mention that it would scare users away if they
saw it).

Cheers
John