abstract: The speed of convergence of the Truncated Realized Covariance (TRC) to the Integrated Covariation between the Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation (iV), through both the degree of dependence and the jump activity indices of the two small jumps processes. To show this, marginal stable-like small jumps with a parametric dependence structure are considered. The estimator is efficient in only some cases of iV jumps. The result of this paper is relevant in financial economics, since by the TRC it is possible to separately estimate the common jumps among two assets, which has important implications in risk management and contagion modeling.