Efforts to make your writing more concise are admirable, but although some words and phrases won’t be missed or fewer or shorter words can be substituted, others may serve a useful distinction. Note, in the following examples and annotations, the differences in the suitability of various phrases.
“What the organization aims to do is produce an economically sustainable model.”
When a sentence describes a series of actions, revise to expunge the weakest among them. Start the sentence with the subject by omitting what, then delete do, and the rest falls into place: “The organization aims to produce an economically sustainable model.”
“I appreciate the fact that we can discuss this reasonably.”
A fact does not need to be identified as such. When such self-referential labeling occurs, delete it: “I appreciate that we can discuss this reasonably.”
“Due to the fact that you arrived late, we missed our flight.”
What does “due to the fact that” mean? “Because.” So use because instead: “Because you arrived late, we missed our flight.”
“We arrived early in order to get good seats.”
“In order to” can easily be reduced to to: “We arrived early to get good seats.” However, sometimes — especially in sentences in which the phrase precedes know or a similar verb — including it seems an improvement on the more concise version.
Retaining the phrase in “She reread the essay in order to understand its argument more clearly,” for example, suggests a contemplation that “She reread the essay to understand its argument more clearly” does not, and “She reread the essay so that she understood its argument more clearly” is the same length as, and no more elegant than, the original wording. “So as to” is a similar construction, as in “We studied other cultures so as to appreciate traditional customs that persist in immigrant communities.”
Also, “in order” is best retained before a negative infinitive, as in “I tiptoed across the room in order not to wake her.”
“I left the papers on my desk in order that I would not forget them.”
“In order that” is equivalent to so and can be replaced by that word: “I left the papers on my desk so I would not forget them.” (That may be retained but is optional.)