We describe the achievement of a significant step in a program whose ultimate goal is a self-consistent model that matches cusp currents from both ionospheric and magnetospheric sources. Building on existing models, we calculate currents that arise from the ionosphere's ohmic response to the interplanetary electric field mapped to the polar cap. Unlike other models, the mapping is confined to the vicinity of the cusp, simulating limited direct communication with the solar wind, as mandated by recent observations. The mapped area is then inserted into the dayside gap of a purely ionospheric expanding polar cap model. The resulting two-cell convection patterns have a pronounced kink in the antisunward flow contours at the poleward boundary of the cusp area, where it joins the expanding polar cap. A similar kink appears in the Heppner-Maynard empirical patterns; the model implies that it marks the boundary where the ionosphere takes control from the solar wind. The model serves as a first tool for identifying Birkeland current types and causes. Three types arise: (1) Currents border the open cusp like region 1 currents bordering a steady state, mini-polar cap. (2) Within the cusp, currents arise from curvature of the equipotentials which, when mapped to the magnetopause, correspond to flow directed away for the merging line, representing merging outflow. (3) The usual region 1 currents line the polar cap boundary along the flow reversals of the two convection cells as a result of polar cap expansion; they are the ionospheric response to the applied electric field. Thus the model predicts two types of region 1 currents, driven directly (1) and indirectly (3) by the solar wind, plus a set of pure cusp currents (2). Together they form the familiar overlapping pattern in the cusp region deduced from observations.