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We show that there exists a very natural, superstatistics-linked extension ofthe central limit theorem (CLT) to deformed exponentials (also calledq-Gaussians): This generalization favorably compares with the one provided byS. Umarov and C. Tsallis [arXiv:cond-mat/0703533], since the latter requires aspecial "q-independence" condition on the data. On the contrary, our CLTproposal applies exactly in the usual conditions in which the classical CLT isused. Moreover, we show that, asymptotically, the q-independence condition isnaturally induced by our version of the CLT.

Central limit theorem, deformed exponentials and superstatistics