Luminous had an idea to try the experiment LaBerg is doing right now. I'll quote the gist of it and have the link at the bottom. It's very simple to do--just sleep in a certain position at night and see if it seems to have a positive affect on your dreaming.
Please give it a try this week!

Sleep Posture, the Nasal Cycle, and Lucidity
For over 1,000 years, the Tibetan Buddhists have been practicing lucid dreaming as a means of approaching enlightenment. In this pursuit, they have developed elaborate techniques for inducing lucidity. Some of these are esoteric beyond the capacity of the uninitiated Western mind to conceive, let alone practice. However, others bear a striking resemblance to the techniques now employed by Western oneironauts, for example, frequent reflection throughout the day on the dreamlike nature of reality.
We are very grateful to the Fetzer Institute, which has provided us with funding to investigate the value of ancient Tibetan lucid dreaming induction techniques in the West. One such avenue which has been little explored to date is that of posture during sleep. Some Tibetan lore suggests that men and women should sleep on opposite sides, "because their energy channels are reversed." We would like to find out to what extent this is so. Previous Lucidity Institute studies on sleep posture, nasal laterality, and lucid dreaming have in fact yielded certain unexpected differences for men and women, but we need more participants to know whether those results were random variations or reproducible.
Awhile back, we offered a different version of this experiment investigating sleep posture and nasal laterality (an ancient Yogic technique for influencing states of mind) requiring a series of early morning naps. Although the nap version of the experiment (LR3060.pdf) was designed to yield the highest rate of lucid dreaming, it evidently was too difficult for most people to schedule into their busy lives. Thus, we have modified the experiment, making it much easier to collect data in the course of one's usual sleeping schedule. We welcome your participation in this new version of the experiment even if you have already completed a previous variation.
http://www.lucidity.com/DreamYoga.html