  The sum of $N$ sufficiently strongly correlated random variables will not in
general be Gaussian distributed in the limit N\to\infty. We revisit examples of
sums x that have recently been put forward as instances of variables obeying a
q-Gaussian law, that is, one of type (cst)\times[1-(1-q)x^2]^{1/(1-q)}. We show
by explicit calculation that the probability distributions in the examples are
actually analytically different from q-Gaussians, in spite of numerically
resembling them very closely. Although q-Gaussians exhibit many interesting
properties, the examples investigated do not support the idea that they play a
special role as limit distributions of correlated sums.
