Adria - The other thing I have done on the days when he isn't getting alot out of the sippy (like Jency Caeden will do fine some days and rotten other days) - I'll use a cup with a straw and he'll do a couple ounces that way - he loves the straw - can't leave him alone with it unless you want a mess, but he does drink good with it!
I have heard too the 16-20 oz total inc other dairy products, as long as he's getting close I think you are all right!