Abstract Polar lows, and mesoscale convective cyclones bearing resemblance to tropical cyclones but originating outside of the tropics, are storms that are challenging to represent accurately in global analyses and models because of their small size, rapid growth at subsynoptic scales, occurrence in data poor oceanic regions, and difficulties in objectively validating them in analysis. Building on previous positive results obtained with respect to the representation of tropical cyclones (TCs) in a global model, a set of observing system experiments (OSEs) performed using the NASA Goddard Earth Observing System (GEOS, version 5) are investigated, focusing on three case studies—a polar low in the Sea of Okhotsk, a polar low in the Southern Ocean, and a Mediterranean Sea tropical-like cyclone that occurred during the boreal fall season of 2014. Experiments assimilating adaptively thinned cloud-cleared hyperspectral infrared radiances from the Atmospheric Infrared Sounder (AIRS) instrument on board the NASA Aqua satellite, with higher density in the vicinity of each storm and its pre-cyclogenesis environment, and lower density elsewhere, demonstrate a positive impact on the analyzed representation of each storm. The adaptive thinning experiments improve the storm intensity and structure, including vertical alignment, depth, symmetry, strength, and compactness of warm core compared to the reference experiments. The results suggest that jet-level processes associated with extremely strong horizontal velocity gradients as represented in the model analysis can be useful to locate dynamically active regions of the extratropical atmosphere where denser data coverage is likely to improve the analyzed representation of polar lows and other similar marine mesoscale convective cyclones. Significance Statement Extratropical maritime mesoscale convective cyclones are short-lived, elusive features that are difficult to represent accurately in global analyses. Previous work by this team demonstrated a positive impact of an adaptive thinning methodology for infrared radiances applied to the tropical cyclone (TC) analysis. The methodology allows a relatively greater volume of radiance data to be assimilated around TCs within a TC-centered moving domain in a global model, yielding an improvement in TC structure and intensity forecast. A similar approach is explored here for two polar lows and a Mediterranean Sea tropical-like cyclone, wherein infrared radiances are more densely assimilated in the vicinity of each storm and its pre-cyclogenesis environment, resulting in a positive impact on the representation of the storm. Strong jet-level horizontal velocity gradients appear to precede each storm, and could be used to automate the adaptive thinning strategy in the future.