In the present study, we examine the factors driving Eurozone sovereign credit default swap (CDS) spreads during the Eurozone sovereign debt crisis. For identifying factors we utilize independent component analysis (ICA), a technique similar to principal component analysis (PCA). We identify three factors that impact spreads and capture the features specific to the crisis such as the breakup risk of the Eurozone: peripheral factor, global factor, and Eurozone common factor. In contrast, when PCA is applied, only a single factor is identified. Moreover, using ICA with a GARCH model, we show that the source of volatility for CDS spreads shifted from the global factor in 2009 and the peripheral factor in 2010 to the Eurozone common factor in 2012, and that the dynamic correlation reflects the decoupling between low credit risk countries such as Germany and high credit risk countries such as Greece. We also show that the goodness-of-fit of the ICA-based model is better than other models used such as the Student's t copula model.