OS: Linux, Windows
shrink, save space, compress
How can I make a .PNG or .ZIP file smaller?
Advancecomp is made for just this.
A good way to use it for zip files:
advzip -z -k -4 *.zip
-z = recompress the specified archives
-k = keep the zip time
-4 = best compression
For png files:
advpng -z -4 *.png
To install on RedHat/Fedora/CentOS:
dnf install advancecomp
There is also pngcrush
In some cases pngnq might help.
In Photoshop you can use "Save For Web".
Uncheck [_] Transparency if you don't need it extra savings.