Is it possible to use image styles in Views field rewriting?
I figured it out! What you have to do is include a copy of the second field, set to "Exclude from display" in the options, and arrange the fields such that Image2 comes before Image1 in the list. You can set the image style in the options for Image2, and that information will get carried over when Image1 is empty and gets rewritten using the behavior specified in the "No results" option. Also, you don't have to write &lt;img src="[field_Image2]"&gt; in the rewrite area.  All you need is the token for the other field, like [field_Image2].