If you have not already check out Bruce Hildebrand's article with tips on cycling. His suggestion to secure our opposable thumb under the bars is spot on.
I also like to suggest that riders who have Shimano brake levers with the inward traveling derailleur cables to use those cables where they come out of the levers as a catch for their thumbs when riding the hoods. This is a particularly aero position for me. Putting the thumbs under the cable will enhance the odds that you will remain with your bike should you hit a bump!
In addition, when riding one handed he suggested placing your hand close to the stem. Good physics here too. If not using a camera but just looking back for your errant dropped cohort or to check out the view or to see if the traffic is peaceful (I never say "clear") I suggest placing your opposite hand under the back of your saddle to secure/leverage yourself down onto the bike. Give it a try. I discovered this technique serendipitously but have never seen it demonstrated or referred to in print though I doubt I was the first to discover this position.
Thanks Bruce for the tips. (I was unable to reply to your article or find a way to write to you directly here though I am not the most sophisticated computer guy!)
I'm not quite getting your explanation on putting your hand under your saddle? Could you go into a little more step by step on what exactly you mean. If I'm interpreting you right do you mean if one is looking over their left shoulder try putting your right hand under the rear of your saddle? May be I'm just having a DUHHHH moment. Thanks.
I think that my use of the word "opposite" might have been confusing or misleading. Sorry.
If you are riding and wish to look back over your right shoulder, keep your left hand on the bar, usually near the center/stem area but then take your right hand and in effect, hook your fingers (probably your index and middle fingers) under the back end of the saddle which will provide a moment of leverage and enhanced stability for the "look see!"
Hope that is better!