I have noticed that when the term "that that" comes up in a sentence, generally one of the "that"s can be removed, and the sentence will retain its meaning. In those cases, I am wondering if there is a preference for one or both "that"s.
For example, "I went to the store. I know that that is true." In this case, the first "that" can be removed and the sentence will retain its meaning. This seems to be true in most cases, but not all.