You may have to look at the assignments more closely. A lot of managers carry such heavy workloads that they habitually plunge into one assignment after another without any thought as to how the tasks should best be handled or what work they should do immediately (think "urgent") and what work can wait. They are working harder and faster than ever before but not necessarily more productively because they spend too little time in thinking through each task first.
A multitude of tasks may pile up, and they all seem to be labeled "urgent." The end result for you is that you are spending too much time putting out fires instead of preventing them. Strategic time management can go a long way toward preventing the forest fires. By "strategic time management," I mean looking at each task from the perspective of its importance to your department’s plans and mission.
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Proceed methodically. Giving a little thought to a situation may enable you to identify a smarter way to handle a problem or situation. More work or longer hours aren’t the solutions to every operational problem. When faced with a last-minute task, pause for a moment. Count to ten before acting. Taking a breath or two may be sufficient to prevent needless wheel spinning and unnecessary pressure. You will have time to consider how the task can be done more efficiently or more effectively, or both. Maybe the work can be outsourced? Perhaps there is another, less expensive way to accomplish the objective? If time is the scarce resource, then there may be a firm that can make up lost time in delivery to your customer?
Stopping to catch your breath will also enable you to determine whether what you have in front of you is a real crisis. Determine what warrants a frantic pace and what can be done in due time, and respond accordingly. Certainly, don’t allow someone who is insecure about your ability to complete a task on time to throw your own priorities out of whack. A realistic view of what is a crisis allows you to make decisions about how to spend your time.