  We present an approach for accurate estimation of the covariance of 2-point
correlation functions that requires fewer mocks than the standard mock-based
covariance. This can be achieved by dividing a set of mocks into jackknife
regions and fitting the correction term first introduced in Mohammad & Percival
(2022), such that the mean of the jackknife covariances corresponds to the one
from the mocks. This extends the model beyond the shot-noise limited regime,
allowing it to be used for denser samples of galaxies. We test the performance
of our fitted jackknife approach, both in terms of accuracy and precision,
using lognormal mocks with varying densities and approximate EZmocks mimicking
the DESI LRG and ELG samples in the redshift range of z = [0.8, 1.2].
  We find that the Mohammad-Percival correction produces a bias in the 2-point
correlation function covariance matrix that grows with number density and that
our fitted jackknife approach does not. We also study the effect of the
covariance on the uncertainty of cosmological parameters by performing a
full-shape analysis. We find that our fitted jackknife approach based on 25
mocks is able to recover unbiased and as precise cosmological parameters as the
ones obtained from a covariance matrix based on 1000 or 1500 mocks, while the
Mohammad-Percival correction produces uncertainties that are twice as large.
The number of mocks required to obtain an accurate estimation of the covariance
for 2-point correlation function is therefore reduced by a factor of 40-60.
