Enhancements of energetic protons (>0.5 MeV) in association with forward-reverse shock pairs have been observed at large heliocentric distances. An interpretation of the time profiles of these events is offered in terms of a model of solar wind stream structure. Persistent sweeping of energetic particles by each shock front and their banking-up by reflection lead to the formation of a gradient along field lines upstream of the shocks. The rise (fall) of intensity before (after) the forward (reverse) shock is explained by a gradient in particle density directed along the upstream field lines toward the shock. A marked intensity decrease between the two shocks is interpreted in the same fashion as being due to parallel density gradients directed toward the shocks. First-order Fermi acceleration upon reflection at each highly oblique shock front offsets loss by leakage through the shock front and sustains the particle intensity in the upstream region. Other acceleration mechanisms may not be required. A simple model is explored in which the gradient profile is primarily determined by a balance between shock sweeping and diffusive flow away from the shock (it is argued that acceleration by reflection and leakage through the shock cause a secondary modification of the profile). Profiles outside the compression region in 15 observations of corotating events suggest a radial mean free path &lgr;r=0.021→0.64 AU (the mean is &lgr;r=0.23 AU) over r=2.6-6 AU. The model predicts an anisotropy which upstream of each shock is lower in magnitude than observations by a factor of ?2. The predicted direction in the upstream region is in the direction of corotation, i.e., perpendicular to the radius vector and counterclockwise in the ecliptic plane. Although net flows in this direction are observed, observations have not generally sought to distinguish upstream from downstream regions where net flows are expected to be approximately reversed.