It looks like the ia's collection of Compute! is complete:

https://archive.org/details/compute-magazine?page=2&sort=dat...

Also Compute!' Gazette:

https://archive.org/details/computes.gazette/Compute_Gazette...

Compute! was very much aimed more at the home market that Byte (which appealed more to IT professionals). At the time, though, Compute! and Compute's Gazette (for Commodore computers) were great for me.

The most amazing magazine of all, though, was The Transactor. Exclusively Commodore, and for programmers. Very few ads, too. Their "Inner Space Anthology" was an incredible resource for everything technical. Memory maps, ROM listings, and much, much more.

https://csbruce.com/cbm/transactor