Offer gifts with purchase. Only gifts or upsells. Nothing else.
Ways to give a gift + discount
There are 3 ways actually to give a discount AND a gift.
1) Using a custom deal with additional gifts, for example: https://automatic-discount.myshopify.com/products/different-discounts-free-gift
2) Using a custom deal "Combined deal" in which you stack 2 custom deals: one called "Gift with purchase" and another custom deal on "whole order" (or on specific products)
3) Using a gift item priced at $0 and automating a discount code, just like that: https://automatic-discount.myshopify.com/products/free-gift