After 13 years office experience, I`ve developed a some kind of urgency sensor.
There are urgent things, and some impossibly urgent things. The impossibly urgent ones are the nice ones, you know that whatever you`ll do, it won`t meet the expectation anyhow, so you can ignore them, as long as there`s the impression you`ve tried to but couldn`t make it.
I even go so far, to calculate the amount of time I could have spent on such work, and spend an equal amount of time on unrelated pleasant tasks/ study.