Continuous single-frequency solid-state lasers with intracavity frequency doubling Nd+3/YVO/KTP, whose frequency is stabilized along the absorption lines of molecular iodine, are currently widely used in laser interferometers. The paper describes a small-sized laser with frequency instability at the level of 10-12 with an averaging time of 1 second. It has been shown that this level of stability is limited by the amplitude noise of the laser, which in turn are determined by fluctuations in the laser pumping. Reducing the amplitude noise and increasing the signal-to-noise ratio in the stabilization system made it possible to further increase the frequency stability of laser radiation.