It's easy to think of constraints as limiting; by definition, they place limitations on what you can do. Especially if you're working creatively, it seems obvious that the more freedom and flexibility you have, the more room you have to be creative. However, I've found the opposite to be the case, and in fact reducing my available options and the number of ways I can be creative has been a very useful creativity-promoting technique.
I think the reason for this is that your brain works very effectively as an optimisation engine. However, each additional dimension, each degree of freedom it has to optimise severely increases the difficulty of that optimisation. It's the reason you don't learn piano by starting with improvisation: the optimisation-space is too large. If you can cut it down to a manageable size, you get much better creative output.
I've found this helpful not just in terms of reducing the complexity of the creative problem, but in reducing unrelated problems. For example, I think if you want to be creative in your work, you should be uncreative in how you work. Trying to compose a sonata on a honkey-tonk piano that you only play at your mate Steve's house on weekends is adding unnecessary difficulty, even if it seems more artsy and creative. A more stable environment makes it easier to be creative within that environment.
So constraints, in the sense of things that constrain the problem space, are more than just a creative trick. In fact, I consider them an essential tool for solving problems.