Some people said that an even fraction downsize avoids the problem. I disagree.
In IE11 I find that reducing an image by 50% (e.g. 300px to 150px) yields a jagged resize (like it's using nearest-neighbor). A resize to ~99% or 73% (e.g. 300px to 276px) yields a smoother image: bilinear or bicubic etc.
In response I've been using images that are just retina-ish: maybe 25% bigger than would be used on a traditional 1:1 pixel mapping screen, so that IE only resizes a bit and doesn't trigger the ugliness.