Great advice, and I think the bit about eliminating the fillers is the most important one for me to remember. I tend to write at length (probably because I'm a chatterbox). If I'm not in too much of a rush, I find the best way to check myself is to write a draft, and then leave it overnight and cut it back the next day. That way, you look at it in a more detached way, and it's easier to see what needs to be cut back.
But I need to actually put this into practice more often!