white noise generation

Hello, newbie here in need of some help:

I'm trying to generate white noise.  I found a paper online called
"Xor****ft RNG's" by George Marsaglia, and found it attractive because of
its simplicity, and its also supposed to generate very good random numbers
that have long periods, pass the diehard randomness tests, etc.  

The problem is, I have a 24-bit codec so I have to shave off 8 bits when I
output the stream as noise.  When I look at the signal analysis of the
output, not only are there unacceptable +/-5dB or so variations, but the
energy RISES at 3dB/octave across the spectrum. (???)

My question is: assuming I have a 32-bit random number generator that is
working properly, should I still see white noise if I only output 24 bits
of that noise?  Or will I get the strange behavior described above?

Any help is much appreciated!