This work addresses the recovery of an image from noisy observations when multiple noisy copies of the image are available. The standard method is to compute the average of these copies. Since the wavelet thresholding technique has been shown to effectively denoise a single noisy copy, it is natural to consider combining these two operations of averaging and thresholding. The first important task is to find the optimal ordering. The second issue is the threshold selection for each method. By modeling the signal wavelet coefficients as Laplacian distributed and the noise as Gaussian, our investigation finds the optimal ordering to depend on the number of available copies and on the signal-to-noise ratio. We propose thresholds that are nearly optimal under the assumed model for each ordering. With the optimal and near-optimal thresholds, the two methods yield very similar performance, and both show considerable improvement over merely averaging.