Mixed shipping based on items and cost?

Here's my desired scenario, and my apologies if this has already been answered (couldn't find a topic here) :

Buy 1-5 items, x fixed cost

Buy 6-10 items, y fixed cost

Buy 11-15 items, z fixed cost

Order of $100 or more, free

So, no problem on the items portion, been doing that for years with a single method. But I can't seem to get a $100/free method to work, override the items, and also automatically select for the customer.

Ideas? Thanks in advance.

I do it via a promotions,


John - Many thanks! I never gave promos a thought, and after testing, it seems like it will do what we need.

CS - It still would be nice if the cost/weight/item options within a shipping method could all be tiered together somehow, instead of all or nothing items, all or nothing cost, etc.

Thanks again, will continue to tweak now that there's a possibility.