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We compute the sphaleron rate in quenched QCD for a temperature $T \simeq1.24~T_c$ from the inversion of the Euclidean lattice time correlator of thetopological charge density. We explore and compare two different strategies:one follows a new approach proposed in this study and consists in extractingthe rate from finite lattice spacing correlators, and then in taking thecontinuum limit at fixed smoothing radius followed by a zero-smoothingextrapolation; the other follows the traditional approach of extracting therate after performing such double extrapolation directly on the correlator. Inboth cases the rate is obtained from a recently-proposed modification of thestandard Backus-Gilbert procedure. The two strategies lead to compatibleestimates within errors, which are then compared to previous results in theliterature at the same or similar temperatures; the new strategy permits toobtain improved results, in terms of statistical and systematic uncertainties.

Sphaleron rate from a modified Backus-Gilbert inversion method