You request more than you need and request it well in advance knowing that sometimes you actually won't have to use it(although it is only requested if something is out there that is a potential problem). That way you have the clearance in hand and can use it without delay which sometimes happens. Of course once past the potential problem with no more potential problems in sight, report Back on Track once you are back on track. Otherwise, you can easily find yourself getting closer and closer to the weather while you are waiting for what are sometimes relatively long delays for the clearance to deviate.
If denied a deviation, make a free text to ATC asking if the deviation might be available at a different altitude.