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The frequency of a 700-mW monolithic nonplanar Nd:YAG ring laser (NPRO) depends, with a large coupling coefficient (megahertz per milliwatt), on the power of its laser-diode pump source. Using this effect, we demonstrate frequency stabilization of a NPRO to a frequency reference by feeding back to the current of its pump diodes. We achieved an error-point frequency noise smaller than 1mHz/ radicalHz and, simultaneously, a reduction of the power noise of the NPRO by 10 dB without an additional power-stabilization feedback system.