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SHORTEN commonly implies reduction in length or duration
CURTAIL generally adds to SHORTEN the idea of docking, a cutting that in some way deprives of completeness
Merriam Webster Unabridged Dictionary
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I think this example from the New York Times shows the approppriateness of the expression:
| Ms. Nagel said she prefers, as do most people, to curtail the length of a personal conversation by saying something like: "I love talking to you but we'll ... |