My suggestions for when you're not interested in stripping your old wallpaper.
Ah, this is an age old question and not one for the purists. I, however, am not a purist and wouldn’t hesitate to wallpaper over wallpaper. BUT - there is a but - only if the wallpaper beneath is in good condition and not embossed or raised or anything like that. The wallpapered wall needs to be completely flat, like lining paper, to do the job well.
Removing wallpaper can be a horrific task (although quite a satisfying one if you’re looking for a bit of therapeutic action) and time consuming so if I was taking on the job, I would definitely check that leaving it as it was and papering over the top wasn’t a possibility before I started. Interestingly, the same applies to paint.
Life ethos: why make life more difficult when it doesn't need to be? Purists, be gone.