Change Excel Zip Compression Level in Windows

You can also through a VBA macro replace the zip engine.
A macro that uses 7Zip to do the compression can be found in the article:
Zip Activeworkbook, Folder, File or Files with 7-Zip (VBA).

Another method which usually gets about 50% improvement in size is by saving the file in the xlsb format that was introduced in Excel 2007. Still another one is to Save As the file, which sometimes reduces its size, presumably by defragmenting.

From the post In which case should we use the xlsm or the xlsb format? :

The difference with xlsb seems to be that the components are not XML-based but are in a binary format: supposedly this is beneficial when working with large files. source

.xlsx loads 4 times longer than .xlsb and saves 2 times slower and has 1.5 times a bigger file. I tested this on a generated worksheet with 10'000 rows * 1'000 columns = 10'000'000 (10^7) cells of simple chained =…+1 formulas

There are also generic methods for reducing the size of an Excel file. See for example:

How to Reduce Size of Excel Files
How to reduce a huge excel file
How to reduce excel file size