I'm trying to build a version of Python *without* debugging information.

The reason for me wanting to do this is because there is a bug which is either in gcc or AIX , that prevents recently patched versions of AIX building code where there are static variables that are unitilized. 

So I have tried 

$ export CFLAGS="-g0"
$export CXXFLAGS="-g0"

The "-g0" should disable debugging information. But instead the option occurs before the automatically inserted options, so I see:

gcc -c -fno-strict-aliasing -g0 -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes  -I. -IInclude -I./Include   -DPy_BUILD_CORE -o Parser/pgen.o Parser/pgen.c

Because of this, the "-g" overrides the "-g0" and I get debugging information. 

Is there any way to not add -g when building Python?

You should override the OPT variable as well. I tried:

$ CFLAGS="" OPT="-fwrapv -O3 -Wall" ./configure

Then "make" shows lines like:

gcc -pthread -c -fno-strict-aliasing  -DNDEBUG -fwrapv -O3 -Wall  -I. -IInclude -I./Include   -DPy_BUILD_CORE -o Modules/python.o ./Modules/python.c

Thank you. That solved it, so you can close this.

Is this worth a README or doc update?

Yes, I think this could do with being documented, as it is not obvious. Generally one would expect CFLAGS to do this, and not OPT.