Morning Jeremy 

Thanks for your question, the 4 – 8mm measurement is for leg height, but there are a few other measurements you need to take into consideration the crown size (across the top) and wire gauge. (thickness) this is why we recommend only using our staples in your Amtech stapler. From your description, it sounds like you have our model no B3770. (bright red) and the correct staple for this is 

B3771 6mm leg height  https://www.amazon.co.uk/gp/product/B00974Z3DE

or B3772 8mm leg height   https://www.amazon.co.uk/gp/product/B00BXH3O66

If your stapler is not red please let me know at contact@dktools.com and I will assist you with links to the correct staples.