In my film The Way I decided to go for a handheld feel for almost the whole film. At the rental house where I borrowed the camera I saw a funny looking steering wheel thing and asked what it was. "Fig rig' they told me, and that noone ever rents it so I should feel free to borrow it. I did, and wow, what a great tool!
Its basically a big steering wheel that you mount the camera on, more or less along the centre axis. It has a couple of advantages. Firstly you can achieve great 'almost-steadycam-shots' following the actors os walking backwards infront of them. Secondly it gives you great access to holding the camera. In the chase sequence I was able to run full tilt ahead of the actors, facing in the same direction of travel, because the rig gave me a handhold on off to the side of the camera so I didn't have to master contortionism to get the shot. For the scenes in the underground the advantage was the fact that I was holding the camera with a wide grip, giving me more stability and control. The rig is also great for low shots. I could hold the camera at the top of the rig, allowing me to keep a fairly upright body position. This meant I could track along, following or leading the actors feet, even at speed.
All in all a great rig for those far-too-frequent productions when you don't have a grip (or even a DOP!)
The Fig rig retails for something like $400 and it's produced by Manfrotto. Well worth it. Of course your local rental house might have one, and chances are no-ones using it as it is strangely unknown.