We study the performance of all-mode-averaging (AMA) when used in conjunction with a locally deflated SAP-preconditioned solver, determining how to optimize the local block sizes and number of deflation fields in order to minimize the computational cost for a given level of overall statistical accuracy. We find that AMA enables a reduction of the statistical error on nucleon charges by a factor of around two at the same cost when compared to the standard method. As a demonstration, we compute the axial, scalar and tensor charges of the nucleon in $N_f=2$ lattice QCD with non-perturbatively O(a)-improved Wilson quarks, using O(10,000) measurements to pursue the signal out to source-sink separations of $t_ssim 1.5$ fm. Our results suggest that the axial charge is suffering from a significant amount (5-10%) of excited-state contamination at source-sink separations of up to $t_ssim 1.2$ fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.
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