Some sentences depend on “that” to make sense, but often you can drop “that” from a sentence with no loss in meaning—and maybe a big gain in voice. On the other hand, when “this” appears in a sentence without an accompanying noun, your readers may puzzle over what “This” is supposed to mean. So see how many “that”s you can drop and if you have a “naked this” you can clothe ….
First version: He said that he’s leaving and that he’s not coming back.
Edited: He said he’s leaving and he’s not coming back.
First version: When I left, I promised to write my friends but never did. This puzzles me now.
Edited: When I left, I promised to write my friends but never did. How quickly I cut those ties puzzles me now.