[jacquesm]

Well, that depends on what you mean by 'work', if with work you mean go up for ever then the answer is a clear 'no'.

However the 'envelope' for just about any balloon that is not built with extreme altitude in mind lies within rather than on top of the atmosphere.

A balloon will go up until the pull of gravity is balanced by the lift, and in most balloons that point will not be reached until the balloon bursts from a lack of counter-pressure by the atmosphere.

[dedward]

Why should they burst? Certainly a little rubber balloon will - but the difference between a good helium balloon and vacuum isn't much - a thin foil layer would contain it without bursting.

[cromulent]

The bursting is a fairly good automatic cut-down. If it doesn't burst, it will ceiling at some point, and then zoom around until something happens.

You might get some more height with a stronger balloon (or a larger balloon with less gas) but you want the flight to be over in a reasonable time if you ever want to get the payload back.

So then you have to use nichrome wire or something as a cutdown, just something else to worry about. 100k-ft is pretty good.