'Tedding' is ok so long as it's not alfalfa. Works fine for grass hay but Tedding alfalfa will knock the leaves off it it, reducing the nutritive value.
Why I just rotary rake it. No tedder though I do own one which sits in the barn 99% of the time. Only time I will use it is after a rain event with crop down to spread it out and let the air get to it, but again, it knocks the leaves off so it's always a compromise at best.