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 Nf=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 ts∼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 ts∼1.2 fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.