The Richardson-Lucy iteration (also known as the EM iteration for image restoration with Poisson statistics) is the most widely used image restoration technique for optical astronomical data. Like all maximum likelihood methods, it suffers from noise amplification in the restored images. Previously suggested methods for dealing with this problem (stopping the iteration early or smoothing the final image) have serious drawbacks for astronomical applications. This paper describes a new image restoration iteration based on the RL method that reduces noise amplification. The method is based on a modified form of the Poisson likelihood function that is flatter in the vicinity of a good fit. The resulting iteration is very similar to the RL iteration, but includes a new spatially adaptive damping factor that prevents noise amplification in regions of the image where a smooth model provides an adequate fit to the data; thus, I call this the `damped Richardson-Lucy iteration.' The damped iteration converges more rapidly than the RL method and can be accelerated using the same techniques as the standard RL iteration. Results are shown for both simulated data and Hubble Space Telescope images.