Resizing to a lower resolution can alter the appearance of an image. In particular, downsampling an image causes blurred regions to appear sharper. It is useful at times to create a downsampled version of the image that gives the same impression as the original, such as for digital camera viewfinders. To understand the effect of blur on image appearance at different image sizes, we conduct a perceptual study examining how much blur must be present in a downsampled image to be perceived the same as the original. We find a complex, but mostly image-independent relationship between matching blur levels in images at different resolutions. The relationship can be explained by a model of the blur magnitude analyzed as a function of spatial frequency. We incorporate this model in a new appearance-preserving downsampling algorithm, which alters blur magnitude locally to create a smaller image that gives the best reproduction of the original image appearance.