Flooring options for upstairs, other than carpet and not noisy

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We want to have the entire flooring changed in a house that we are buying.
For many reasons, we have decided to have no carpet anywhere in the house.

That is ok for downstairs. But, we are worried that it will be noisy if we put anything other than carpets upstairs..the kind of noise when someone walks upstairs..We have had that in houses where there is carpet. But, we hear generally that it is less if the flooring is carpeted. we don't wear shoes inside, but still, it gets noisy.

Sure, there must be solutions out there..
Better underlay? Or can some sort of pre-treatment be done to the flooring ?
Any other ways to reduce the noise...

Thanks

I'll be interested to see what people suggest too. We currently have bare floorboards and it's fine but I guess there are two issues. One is that hard floors make more noise and the other is that carpet usually has underlay so that adds an extra absorbing layer. So, bare floorboards would be the worst for noise as they are hard and (usually) have no insulation. If you put a new wooden floor you could probably add cork underlay which would absorb more sound. Or you could go for a softer material like vinyl - amtico seems popular here.

We are thinking of tearing out the bedroom carpets and replacing with laminate and felt underlay.

I hate carpet and dog likes throwing up on it from time to time (always in wee small hours of the morning for some strange reason). Much easier to clean up with laminate.

We do have the original Victorian floorboards, but they are pretty crappy and the previous owners painted both bedroom floors gloss white............

You can put good underlay under the laminate with rugs if need be. We had laminate in our first floor flat and it wasn't too bad for sound (we knew our neighbours and I've been in their flat and heard dh upstairs but only closing the door, not foot steps). However I didn't let the kids run about on it!