This paper tackles the problem of detecting abrupt changes in the mean of a heteroscedastic signal by model selection, without knowledge on the variations of the noise. Whereas most existing methods are not robust to heteroscedasticity, a new family of algorithms is proposed showing that cross-validation methods can be successful in this framework. The robustness to heteroscedasticity of the new cross-validation based change-point detection algorithms is supported by an extensive simulation study, together with recent theoretical results. An application to comparative genomic hybridization data is provided, showing that robustness to heteroscedasticity can indeed be required for their analysis.