How to fix visibility for out-of-stock products?

My out-of-stock products are messing up product count and pagination.
They are not showing but they count in the product count on archive pages and pagination is off.

Example: “Showing all 5 results” but 3 products are showing.
Example: 3 paginated pages and the last page is empty.
Example: categories showing even though no products in them (all are out-of-stock)

How can this be fixed?
One workaround is:
1. Set stock to 1 for an out-of-stock product
2. Save
3. Set stock to 0
4. Save
Now that product is not counted.
But I would love to see an automated approach. ??

Thanks!