How do I reduce the size of epub?

Any advice on reducing the size of an epub? The beta validator requires a size 10 MB or less. My current export is 10.5 MB.

In searching online, one recommendation was to change the settings on the export dialog box to 96 ppi and med-low resolution, which I did, but the epub still exported to the same size.

Another suggestion was to change the extension file from .epub to .zip, and then "unzip" the file and drag the images to a program called imageOptim, which I downloaded but after changing the extension and clicking on it, it said "unsupported file format" and wouldn't unzip.

Right now I'm considering opening up all the images in Photoshop and changing them from 300 ppi to 150 ppi in a new layout just for the epub. Anyone have any alternatives or any insight as to why the export settings didn't work? Thanks.