FitCov estimates the covariance of two-point correlation functions in a way that requires fewer mocks than the standard mock-based covariance. Rather than using an analytically fixed correction to some terms that enter the jackknife covariance matrix, the code fits the correction to a mock-based covariance obtained from a small number of mocks. The fitted jackknife covariance remains unbiased, an improvement over other methods, performs well both in terms of precision (unbiased constraints) and accuracy (similar uncertainties), and requires significant less computational power. In addition, FitCov can be easily implemented on top of the standard jackknife covariance computation.