Fine-grained magnetic particles in deep-sea sediments often statistically align with the ambient magnetic field during (and shortly after) deposition and can therefore record geomagnetic reversals. Correlation of these reversals to a geomagnetic polarity time scale is an important geochronological tool that facilitates precise stratigraphic correlation and dating of geological records globally. Sediments often carry a remanence strong enough for confident identification of polarity reversals, but in some cases a low signal-to-noise ratio prevents the construction of a reliable and robust magnetostratigraphy. Here we implement a data-filtering protocol, which can be integrated with the UPmag software package, to automatically reduce the maximum angular deviation and statistically mask noisy data and outliers deemed unsuitable for magnetostratigraphic interpretation. This protocol thus extracts a clearer signal from weakly magnetized sediments recovered at Integrated Ocean Drilling Program (IODP) Expedition 342 Site U1406 (Newfoundland margin, northwest Atlantic Ocean). The resulting magnetostratigraphy, in combination with shipboard and shore-based biostratigraphy, provides an age model for the study interval from IODP Site U1406 between Chrons C6Ar and C9n (approximate to 21-27 Ma). We identify rarely observed geomagnetic directional changes within Chrons C6Br, C7r, and C7Ar, and perhaps within Subchron C8n.1n. Our magnetostratigraphy dates three intervals of unusual stratigraphic behavior within the sediment drifts at IODP Site U1406 on the Newfoundland margin. These lithostratigraphic changes are broadly concurrent with the coldest climatic phases of the middle Oligocene to early Miocene and we hypothesize that they reflect changes in bottom water circulation.