Hydroxyapatite
The stuff your enamel is made of, as a toothpaste without fluoride. You choose it not because fluoride fails, but because fluoride builds up somewhere you would rather it did not.
How to use it
As your daily toothpaste, twice a day, in place of your fluoride paste. Not alongside it and not alternating: then you know what neither of them is doing.
The best version
A paste that names hydroxyapatite as a main ingredient and gives a percentage. If it only says "with hydroxyapatite" and no number, you are buying a claim.
How to prepare it
Brush and spit, do not rinse. Rinsing washes the paste away before it has done anything, and that holds for fluoride just as much.
What it does
You give nothing up for it. In an eighteen-month double-blinded trial in adults, a fluoride-free hydroxyapatite paste was compared with a paste containing 1450 ppm sodium fluoride. In 89.3 percent of the hydroxyapatite group no new decay or filling appeared at all, against 87.4 percent in the fluoride group. That gap was small enough to call the paste not inferior.
The reason to want an alternative is where fluoride ends up. In eleven aged cadavers the pineal gland was measured, the gland that makes your melatonin: it held 297 mg of fluoride per kilo, against 0.5 mg per kilo in muscle from the same body. The fluoride in that gland tracked the calcium in it, and its fluoride to calcium ratio was higher than in bone.
Luke J. Fluoride deposition in the aged human pineal gland. Caries Research, 2001.
Watch out
That study shows it accumulates, not that you notice anything. No human study links calcification of the pineal gland to worse sleep or to less melatonin because of fluoride. This is a good reason to want an alternative and not proven harm.
Four of the authors of the toothpaste trial work for the company that makes the tested paste. That does not make the result untrue, and it does mean more than one independent trial is needed before this is settled.
It is one trial, in adults, over eighteen months. Fluoride has decades of research behind it. If you get a lot of decay or you are at raised risk, this is a conversation with your dentist rather than a choice in an aisle.