I downloaded the Windows 2.5b1, and then tried to 
install following all defaults.

I had previously installed 2.5a2, and it is possible 
that I switched between "install for all users" and 
"install just for me".

The install offered me a finish button, and no protest 
when I clicked it -- but after that, the shortcuts did 
not start python (nor did they protest; they just went 
into never neverland).  Starting python at the command 
line did work.

Reinstall with a repair did not fix anything.

Uninstall, then uninstall 2.5a, then install on a 
"clean" system did work.

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Can you please give a precise reference to what you've
downloaded?

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All versions are binary downloads for windows, from 
python.org

I have a 2.4, which seems not to be relevant.

I don't remember whether I had installed 2.5a1, though I 
think so.  If I had, it was successfully overwritten by 
2.5a2.

I had definately installed 2.5a2.

The problem came when I attempted to install 2.5b1 on top 
of 2.5a2.

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I could not reproduce the problem. Can you please try to
reproduce it, installing things in the order you did? Please
provide all details, such as sequence of MSI invocations,
options selected, reboots/logouts performed, etc.

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I can no longer locate the alpha installers, but I'll see 
if I can reproduce it with the beta installer plus a 2.4 
version.

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The alpha installers are at

http://www.python.org/ftp/python/2.5/prev/

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Closing this as "works for me". If it happens again, please 
create a new report with the exact steps needed to 
reproduce.