Resting-state functional MRI (fMRI) provides a crucial insight into brain organization, by offering a mean to measure the functional connectivity between brain regions. A popular measure, the effective functional connectivity, is derived from the precision matrix obtained by inverting the correlations between brain regions fMRI signals. This approach has been widely adopted to build brain connectomes for large populations. For small populations and single fMRI scans, however, the significant amount of noise in the fMRI scans reduces the quality of the precision matrices, and the non-invertibility of the correlation matrices calls for more sophisticated precision estimators. These issues are especially dramatic at full brain resolution. In this work, we investigate several approaches to improve full resolution precision matrices derived from single fMRI scans. First, we compare three approaches for the computation of the correlation matrix. Then, we investigate two regularized inversions, in combination with a correlation shrinkage and two spatial smoothing strategies. During these experiments, the quality of precision matrices obtained for random fMRI half scans was measured by their generalization: their fit to the unseen time points. Our experiments, using ten high resolutions scans of the Human Connectome Project, indicate that correlation shrinkage strongly improves precision generalization. The two regularizations are associated with similar generalization. Smoothing the fMRI signal before the inversion deteriorates the generalization whereas a penalty directly improving the smoothness of the precision matrix can improve the generalization, in particular for short time series and in combination with shrinkage.