If you avoid doing stuff you hate, the cloud of having to do it lingers over you; you are not really avoiding it, you are prolonging it. Just get it over with and move on. You'll deliver it on time (or earlier), and will have gotten past the hurdle.
More generally, boring = automatable. If the code that you are writing, or the other task you are doing is boring, it is ripe for automating - so automate it! You'll never have to do the boring task again.
See http://news.ycombinator.com/item?id=254513
I like your do-the-dull-stuff-first philosophy. But you can't discount the fact that we stay in dull, drab workplaces as a matter of choice.
If you hate your work we each have the choice to go somewhere else. Be an electrician, or a garbage collector. Move to a different company that offers more compelling work, or start one that does!
I'm just saying we do have the choice to do work we enjoy, even if it means we sacrifice some security to drop the status quo and never look back.
Free trade.
If it's a job you have, then talk to your boss about what projects you would be excited to do, and see if you could work together to change the dull/exciting mix. Offer to work extra on the exciting/challenging project to prove your capabilities if that's a necessary step.
We had a programmer who was often on 'dull' assignments worked nights on a really big problem our company was having - our new product was sluggish, and needed some serious redesign. He spent a month working on a proof of concept on his own time, and then presented it to his boss, and then the programming team.
Now he's working on future architectures and pretty high level, fun and interesting stuff.
It's dull enough to post for help on a newsgroup. Do something about it. Change your trajectory.
I like to sit down with users and talk with them. Pour a cup of coffee and talk. You'll get the coolest stories and usually, when the 3rd cup is empty, you know exactly what needs fixing. You may program computers, but the point is to shape that friggin' turing machine equivalent so it helps people.