When compared to quiet land stations, the very broadband Monterey ocean bottom seismic station (MOBB) shows increased long-period background as well as signal-generated noise. Both sources of noise are unavoidable in shallow ocean bottom installations, and postprocessing is required to remove them from seismic observations. The long-period background noise observed for periods longer than 20 s is mainly due to infragravity waves and ocean currents. The shorter-period signal-generated noise, on the other hand, is due to reverberations of the seismic waves in the shallow sedimentary layers as well as in the water layer. We first present the steps that were taken prior to and during the instrument deployment to minimize instrument generated noise as well as to avoid noise due to water flow around the instrument. We then present results from two postprocessing methods that can be used to remove the long-period background noise, which both utilize the ocean bottom pressure signal locally recorded on a differential pressure gauge (DPG). One consists of subtracting the locally recorded ocean bottom pressure from the vertical seismic acceleration signal. In this case the frequency-independent scale factor is linearly estimated from the data. The other one makes use of the transfer function between the vertical seismic and pressure signal to predict the vertical component deformation signal. The predicted signal is then removed from the vertical seismic data in either frequency or time domain. We also present two methods that can be used to remove the signal-generated noise. One employs the empirical transfer function constructed from MOBB data and nearby land station data that do not show the signal-generated noise. The other one uses a synthetic transfer function computed by modeling the response of shallow layers at the MOBB location. Using either of the two transfer functions, most of the signal-generated noise can be removed from the MOBB data by deconvolution.