Low-frequency (<0.1 Hz) vertical-component seismic noise can be reduced by 25 dB or more at seafloor seismic stations by subtracting the coherent signals derived from (1) horizontal seismic observations associated with tilt noise, and (2) pressure measurements related to infragravity waves. The reduction in effective noise levels is largest for the poorest stations: sites with soft sediments, high currents, shallow water, or a poorly leveled seismometer. The importance of precise leveling is evident in our measurements: low-frequency background vertical seismic spectra measured on a seafloor seismometer leveled to within 1 × 10-4 radians (0.006 degrees) are up to 20 dB quieter than on a nearby seismometer leveled to within 3 × 10-3 radians (0.2 degrees). The noise on the less precisely leveled sensor increases with decreasing frequency and is correlated with ocean tides, indicating that it is caused by tilting due to seafloor currents flowing across the instrument. At low frequencies, this tilting generates a seismic signal by changing the gravitational attraction on the geophones as they rotate with respect to the earth's gravitational field. The effect is much stronger on the horizontal components than on the vertical, allowing significant reduction in vertical-component noise by subtracting the coherent horizontal component noise. This technique reduces the low-frequency vertical noise on the less-precisely leveled seismometer to below the noise level on the precisely leveled seismometer. The same technique can also be used to remove “background” noise due to the seafloor pressure field (up to 25 dB noise reduction near 0.02 Hz) and possibly due to other parameters such as temperature variations.