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The first example you offer, a "strike-through" on completed tasks, is already possible. Open the Project: Styles inspector. On the left side, select "Completed Tasks" from the list. Click "Choose Font.." on the right. In the font pane that appears, look for the T with a strike-through on it. From that menu you can choose a single or double strike-through. This doesn't cover the "deadline way in the future" cases you mention, though.

If you're running OmniPlan 1.5, you can also hide tasks temporarily by applying filtering rules. Choose "Filter Tasks" from the View menu. Here you can create rules for filtering (sort of like Mail's filtering rules interface). You can choose to show only tasks whose end date is within the next two weeks or are assigned to Joe, or are incomplete, or all of the above.

We are looking to improve both of these features, so please make specific lists of what styling and filtering options you'd like added, and email them to us. (omniplan@omnigroup.com)