We develop models for portfolio diversification in the sovereign credit default swaps (CDS) markets and show that, despite literature findings that sovereign CDS spreads are affected by global factors, there is sufficient idiosyncratic risk to be diversified. However, we identify regime switching in the times series of CDS spreads and spread returns, and the optimal diversified strategies can be regime dependent. The developed models trade off the CVaR risk measure against expected return, consistently with the statistical properties of spreads. We consider three investment strategies suited for different CDS market participants: for investors with long positions, speculators that hold uncovered long and short positions, and hedgers with covered long and short exposures. We use the models to illustrate that diversification pays in the CDS market. The models are also tested for active portfolio management in Eurozone core and periphery, and Central, Eastern and South-Eastern Europe countries, and the optimized portfolio results outperform the broad S&P/ISDA Eurozone Developed Nation Sovereign CDS index. The paper concludes by identifying open questions in developing integrated enterprise-wide risk management models using CDS.