I just had a mom with the common combination -- pendulous breasts, flattish nipples, and a sleepy baby.  She was three days postpartum, and infant still had not nursed well.  Working on waking the baby, mom observed, "you know, we seem to get him so wide-awake, then we put him to the breast and he immediately seems to fall asleep."  Guess what positions they were trying to feed in.  So we had mom sit bolt upright, with baby almost straddling her leg, facing her breast, and . . .  You got it, the baby latched on, stayed on and nursed vigorously about half and hour, then did another 15 minutes plus on the other breast -- same position.

Patricia, in Milwaukee, maybe your baby would receive a double benefit from this posture -- less sleepiness, and less choking.  

Sincerely, Chanita, San Francisco