1) Create a work folder (e.g. Compress), keep the original version of the PowerPoint file and created one version that you will compressed. Create also "pictures" folder for working with the pictures.
2) Rename the file that will be compressed to zip.
3) Double click the zip file and drill down to the "media" folder:
4) Sort the files by the size by clicking the "Compressed size" heading:
5) Copy all the files over 1000 KB to the "pictures" folder:
6) Open "paint.net" program and open a picture from your "pictures" folder:
7) Resize the picture by a percent value and save it:
8) Repeat steps 6 and 7 for all the pictures in the "pictures" folder. The size of the picture files should now be much smaller:
9) Copy the picture files from the "pictures" folder and paste them into the "media" folder of the zip file:
10) Rename the zip file to pptx:
11) Open the PowerPoint presentation and check that it looks good.
It might be necessary to repeat the steps above several times. If some of the shrinked pictured do not look good, the original pptx file can be renamed to "zip" and the original pictures can be copied from its "media" folder. The pictures can then be shrinked to a higher percentage then before. Repeat the process of shrinking the pictures and checking whether the adjusted pptx file has the right size and looks good at the same time.
"paint.net" can be downloaded here: Download (dotpdn.com)