I have done some of my best job under pressure and deadlines. Thing is, that pressure, those deadlines, they were not imposed from the outside. They were consequences of me feeling responsible for a project, a document, a team, a deliverable.
If you impose pressure and deadlines, particularly when you do not share clear reasoning (as in “we do this because it helps us this way”), people might still do the job. Great job, though, needs internalization.