It's important to understand that there is a difference between what you do when you're learning a move and what you do when you're performing a move that you've already learned.
To learn the one-hand top palm, go ahead and practice the basic action by side-jogging the top card a small amount over the right side of the deck. You eventually won't need to do this, but it's a good way to get a feel for the action.
This side-jogging of the top card does 2 things: First of all, it enables the right pinky to push down on the exposed upper right corner of the card. This gives you the necessary leverage to maneuver the card up and into the palm. Second, it allows for a tiny bit of extra clearance at the lower left end of the deck where the right thumb is positioned. Sometimes the corner of the card can hang up on the thumb during the execution of the sleight. The small side-jog helps to prevent this.
Start off with perhaps twice the width of a white border. Over time, reduce this to the width of the border. Eventually, you'll be able to eliminate the side-jog entirely.
And of course, there's very few things in card magic that won't work themselves out with a few hundred thousand repetitions.
Jason