Show price without VAT for non-EU customers


I have a site that sells mobile phones worldwide, applying VAT to orders within the EU and no VAT to orders outside.

Currently, I’m adding prices including the tax. I’ve set up the relevant locations and tax rates, which seem to be working correctly: I can show the price including and excluding tax on the category listing, and the display changes if a non-EU user is logged in.

But there’s one problem: the system clearly understands that it should show only one price for non-EU users, but the price it shows includes the VAT. If the tax rate is zero for that location, surely it should remove the tax from the price that the customer pays?

Is there another way to set that up so that it works, I wonder? Any help will be gratefully received…

Many thanks,