The location of the high-latitude boundary for magnetospheric convection to the dayside on almost-dipolar field lines cannot be arbitrarily selected. The correct choice is near the high-latitude boundary of the composite Alfv¿n layer (the thick layer for a distribution of particle energies). It is argued that other choices lead to extensive regions of &bgr;>1 plasma and hence are unphysical. Differences, supported by observation, in the resulting convection model include no gaps between Birkeland current sheets, no plateau in electric field measurements across the auroral zones, the existence of a strong Harang discontinuity on the nightside, and the movement of the convection region to lower latitudes with increasing cross-magnetosphere potential. The above theoretical boundary is related to observed boundaries. ¿ American Geophysical Union 1988