Burping a lot/ getting too much air?

Any tips for decreasing the amount of air a breastfed baby swallows while nursing? My daughter is three weeks old. I burp her after she nurses on each side, but she has to burp a LOT. She will burp at least two times right after nursing on each side, and then when I lie her down to sleep, she will often wake up and start grunting and fussing about an hour later and then have to burp some more. I've had no luck getting these "extra" burps out the first time around. A lactation consultant visited us twice in the hospital and said her latch looks great. I breastfed my son for 16 months and didn't have this problem. Any advice? This is making it hard for both of us to sleep!