  We demonstrate a method to reduce number fluctuations in an ultracold atomic
sample using real-time feedback. By measuring the Faraday rotation of an
off-resonant probe laser beam with a pair of avalanche photodetectors in a
polarimetric setup we produce a measurement that is a proxy for the number of
atoms in the sample. We iteratively remove a fraction of the excess atoms from
the sample to converge on a target proxy value in a way that is insensitive to
environmental perturbations. We demonstrate a reduction in the number
fluctuations from more than $6\%$ to only $1.3\%$ for samples at temperatures
of 15 $\mu$K and 2.8 $\mu$K over the time-scale of several hours.
