The eigenspectrum for jackknife shrinkage, debiased jackknife, and DICES (a combination of both with the jackknife shrinkage correlation structure with debiased jackknife standard deviation) computed from N_JK = 74 and compared to the eigenspectrum of the sample covariance (dashed black line). In the bottom subplot we show the ratio with respect to the sample covariance. The solid lines represents the mean and the envelopes the spread (i.e. 95% confidence interval) from ten realisations. Linear shrinkage produces a covariance estimate that is non-singular but biased high, while the debiased jackknife is singular and has a poor non-diagonal structure. The combination resolves the deficiency of both methods, providing a covariance that is non-singular and unbiased.