Beaver dam, northern California, USA
Back at the end of May, a beaver dam failed upstream of the town of Warren, flooding the place and causing a fair amount of damage. They started cleaning up, but really didn't do anything about the root of the problem. Sure enough, it failed again a couple of weeks ago, causing more damage. Now the residents want all of the beavers trapped out and killed. That's idiotic; for one thing, more will simply move in. Besides, the little engineers provide substantial benefits for fish and other wildlife.
What they should do is fairly simple, though it involves a bit of understanding of the behavioral biology of the critters. You hike up to the dam and determine what level of retention pond depth seems reasonable, then you chop holes in the dam to achieve your optimal level. Beavers, however, are attracted to the sound of running water and to currents, and will quickly - often overnight - repair any damage to their structure. This is where you need to be smarter than the beaver.
Into each of your cuts, place a length of PVC pipe, capped at both ends with a 90-degree elbow pointing downward. One end of the pipe, with its downward-pointing elbow, is thrust against the back of the dam itself; the rest of the pipe, with the other downward-pointing elbow, extends out into the pond itself. Leave.
When you return, you'll find that the pipes have been effectively cemented into place by the beavers themselves as they've repaired the cuts you made. The dam is back to its usual height, but water is released by the pipes, through the dam, where it runs harmlessly down the back of the dam and rejoins the stream. Problem solved, with minimal effort and expenditure. No beavers were harmed in the production of this solution.