How important are original box & papers?

Would you take a vintage/vintage-ish piece that comes without the original box, papers, and straps, etc., at a discounted price? Or would you rather pay the premium to have all the components in place?

How important are the original box & papers -- should a lack of them be a deal breaker?

All comments and advice are appreciated!

Cheers,
coffee

For new/nearly new pieces - essential.
For vintage pieces - I'm happy to overlook papers in favour of a good price.

Straps are an almost non-issue for me.

I would pay more for a piece with box and papers. It's an easier re-sell if you want to move it on later, plus f someone has kept them, it's a strong indication that they look after things (including, hopefully the watch!). But box and papers isn't usually a deal-breaker for me. I've bought pieces without them.

I like to have box and papers, but not having them isn't the end of the world for me.

For vintage watches, the box and papers and certainly worth a premium. You might pay $1500 upwards for a separate box and blank papers...and even then, they're blank and not specific to the watch. Must admit that early on in my collecting days I bought a crappy Heuer 1000 because it came with a brand new box. I then sold the box for about twice what I paid for the box plus watch!

Certainly not a deal breaker, but a nice to have, and one that does command a higher price.