After a lot of research, I found the perfect harness for small dogs at the Italian maker Tre-Ponti. Their mesh buckle harnesses are designed to evenly distribute the pressure points over the whole structure. They’re easy to put on and they don't catch your dog's fur under the armpits. The material is breathable and lightweight allowing your dog maximum movement, and they can be easily washed.
In my shop I offer size two, which is perfect for dogs between 4 and 5 kgs (my miniature dachshunds weigh just 4 kg each, but because of a dachshund's wide chest, taking half a size up makes a perfect fit).