Hedging

You are hedging if you refine your claim simply to avoid counterevidence and then act as if your revised claim is the same as the original.

Example:

Samantha: David is a totally selfish person.
Yvonne: I thought we was a boy scout leader. Don’t you have to give a lot of your time for that?
Samantha: Well, David’s totally selfish about what he gives money to. He won’t spend a dime on anyone else.
Yvonne: I saw him bidding on things at the high school auction fundraiser.
Samantha: Well, except for that he’s totally selfish about money.

You don’t commit the fallacy if you explicitly accept the counterevidence, admit that your original claim is incorrect, and then revise it so that it avoids that counterevidence.