The influence of bottom topography on the westward propagation of long, baroclinic Rossby waves is studied analytically in a two-layer ocean model. In the limit of a thin upper layer, scaling analysis suggests that the waves should be relatively insensitive to variable bottom topography however, this insensitivity can break down in regions of closed f/H contours, where f is the Coriolis parameter and H the ocean depth. An integral constraint is derived in the planetary-geostrophic limit, showing that the net radiative flux of upper layer thickness anomalies into a closed f/H contour, at its eastern margin, is balanced by an equivalent radiation of upper layer thickness anomalies out of the closed f/H contour, at its western margin. The consequence of this, and a related integral constraint for the upper layer thickness tendency, is that westward-propagating upper layer thickness anomalies can partially disappear on one side of a closed f/H contour and, near instantaneously, reappear on the other — a "Rossby wormhole." In practice, this partial jumping of westward propagating upper layer thickness anomalies across an f/H contour is accomplished by conversions between the baroclinic and barotropic wave modes, and the generation of transient barotropic recirculations around the f/H contour. The Rossby wormhole mechanism is illustrated in a series of numerical calculations with a two-layer primitive equation model. A corollary is that the reduced-gravity model of the large-scale ocean circulation can break down in the presence of closed f/H contours, even when the conventional scaling requirements for its validity appear to be satisfied.