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The stabilizing mechanism of a single-frequency compound-ring erbium-doped fiber laser is greatly improved by canceling the associated frequency dithering. This is achieved by exploiting the filter feature of an optical fiber compound-ring resonator to produce a net resultant intensity modulation. The theory of this cancellation method, derived from the phase resonant condition of the compound-ring resonator, shows that a full cancellation of the frequency dithering can be attained when two antiphase dithers are applied. Experimentally, the frequency jitter of the laser is greatly suppressed and the linewidth is less than 5 kHz.