How do I measure and cut the new stair treads to be snug?

I don't think they're intended to be snug to allow for contraction and expansion. Depending on your stair configuration I would think that a snug board would push on stuff it shouldn't push on when it did expand. It could have been Tom Silva a saw that cut the steps just shy of 90 to allow for ease of dropping them in place between the base board on one side and the ballaster base on the other side.

Just because these perpendicular boards look straight doesn't mean they really are and a little ease between the board you are laying and them would be a good thing, easily covered with shoe molding. More.

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