I just acquired some new very inexpensive Basswood, and some of the pieces were understandably not as nice as others. What I mean is that some of the boards included lots of heart wood (darker). Most of the wood was sap wood (white), which is easier to carve. I think the darker heart wood is harder and more difficult to carve. The reason I made the purchase was because I did not want to spend very much, so I really do not want to throw away or burn the boards that contained the heart wood. I just had to save it.
This is one way to save hard Basswood. You can add moisture to make it easier to carve.
Piece on the left is white sap wood, and easy to carve.
Piece on the right is dark heart wood and difficult to carve because it's a bit harder than the sap wood.
To soften the darker heart wood, place it in a plastic bag along with a damp paper towel, for several hours (6).
After several hours the heart wood will have absorbed enough moisture to make it carve a bit easier.