Lerch that was a good reply. It's pretty much the way it is.
To add my 2cents, besides making the shooting experience more comfortable which is a good thing, the palm swell, in my opinion, tends to keep the hand "indexed" the same for each shot. It also tends to keep the elbow indexed the same, especially prone, for me.
My feelings are that the swells, I put 'em on both sides and use a thumbhole stock, should fit 'your' hand. When someone shoulders my 'Big Girl' from both sides the first thing they say is that the swells are different. That's because "my" hands are different. And so are your's especially the left hand. Its way more different than the right.
Regarding swells on both sides: With two eyes, two trigger fingers and two shoulders, I shoot from both sides which greatly improves the degrees of freedom when the shot opportunity arrives. Note, this is mostly from the prone position.
Also please forgive the stock foo paws, she's going back on the bench for a refinish job this spring.