In this work, we investigate the effects of the width of an annular baffle region on natural convection heat transfer to an immersed, coiled heat exchanger in an otherwise quiescent sensible hot water storage tank. In experiments, the coiled heat exchanger sits in an annular region created by the tank wall and a straight, cylindrical baffle. The width of this baffle region is 1.5, 2, 3, or 4 times the heat exchanger diameter, These experiments are compared to each other and to corresponding control experiments with no baffle. In general, all baffles create considerable benefits over their respective control experiments, consistent with past studies. The considered metrics of heat transfer rate, fraction of energy discharged from the tank, and heat exchanger outlet temperature show that heat transfer is improved slightly by narrowing the baffle region. For example, relative to their respective controls, the energy extracted from the tank after 30 min of discharge in the 1.5D, 2D, 3D and 4D experiments is 23.2%, 20.8%, 18.1%, and 14.7% higher, respectively. This improvement in natural convection heat transfer as the baffle region narrows is attributed to the increasing thermal stratification observed in experiments with increasingly narrow baffle regions.