A while back I heard the story of how to fit many stones into a container. Start by adding the biggest ones, then smaller until the container is full. Adding in the reverse order will end up filling the container much faster with less getting in.
This is a lot like our day, but I think the base analogy and our lives have to be adjusted a bit. The higher the priority, the larger the pebble. You can't totally fill things with the high priority items or you will only be able to fit in a few low priority items.
Instead, do things in layers. Do a couple high priority things, then some medium and finally some low priority items. Repeat this process and you will fill the container that is your day with much more. It will allow you to accomplish many things, but to be much more efficient about it.
Some high priority items may not get done as fast as they should, but it will all get done quicker overall.
The only tricky part with applying this to life is that things keep being added to our incoming pile. We just have to adapt to this and live with a layered approach to get more things done.
At least that is my theory now!