Out of memory in Bryce 7! !                              Could that be fix.

I find that it is needful to frequently hit the save button and close the file and then re-open it, especially if there are a lot of objects in the scene. Reducing the poly count on individual objects such as rocks, terrains etc is also helpful as is not going overboard with the sky editor effects.

Using smaller textures helps too.

Keep saving! 

You can free up some space by deleting things you don't need.  For example, if you imported a human figure into the scene you may be able to delete body parts hidden underneath clothing or on the side of the figure facing away from the camera, teeth if the mouth is closed, etc.

In addition to resizing images smaller like TheBryster said, you may also be able to delete some images entirely and just use basic materials instead.  No point in having a 2000x2000 pixel image texture for something 10 pixels wide in the background.

You may also want to use Large Address Aware if appropriate, that might give you a tiny bit of extra available memory under certain circumstances.

I haven't taken the time to see how much memory it might free up, but if you use instances instead of copies for identical objects, that should help some.

There was something I recall from a while ago. It's called affinity and if checked it will - on a multi-core pc - use all the processores for brycing. I dont remember where it is though.