We analyze the performance of a single, long-lived, Compound TCP (CTCP) connection in the presence of random packet losses. CTCP is a new version of TCP implemented in Microsoft Windows to improve the performance on networks with large bandwidth delay-products. We derive a Markovian model for the CTCP sending window and compute the steady state distribution of the window and the average throughput of a CTCP connection. We observe that the previous approximation, using a ``typical cycle", underestimates the average window and its variance while the Markovian model gives more accurate results. We use our model to compare CTCP and TCP Reno. We notice that CTCP gives always a throughput equal or greater than Reno, while relative performance in terms of jitter depends on the specific network scenario: CTCP generates more jitter for moderate-high drop rate values, while the opposite is true for low drop rate values.