Z-Fighting on Composite Model

Title pretty much says it all. I'm trying to make tool trims for my resource pack, and I used the composite model type. This causes some noticeable Z-fighting on the edges though.
I checked if this was the case for trimmed armors in item form, and it is, so it seems like an issue on minecraft's end.
Is there any way to fix this? At least with the armor trims, it's not very noticeable.. with my weapon trims.. well there's a lot of exposed edges. ;(