Spacecraft measurements over the past two sunspot cycles have shown that the average strength of the interplanetary magnetic field (IMF) undergoes surprisingly modest long-term variation, unlike the total magnetic flux observed on the Sun. Our attempt to model the IMF during sunspot cycle 21, based on a current-free extrapolation of the observed photospheric field out to a fixed source surface where the field lines become radial, yields calculated IMF intensities which vary by an order of magnitude and which are far too low near sunspot minimum. We obtain much better agreement with a model containing both heliospheric sheet currents, which deflect polar flux toward the ecliptic, and volume currents, which maintain a residual latitudinal gradient in the IMF intensity. In order to match the observed IMF intensity levels, however, the measured photospheric fields had to be scaled up by approximately a factor of 2. Our composite model has the following main consequences: (1) The source of the radial component of the IMF may be represented to a first approximation by the dipole component of the photospheric field. (2) The radial IMF intensity is strongest in the direction of the dipole axis, which is aligned with the Sun's rotation axis near sunspot minimum but tilts toward the ecliptic near sunspot maximum. (3) The average strength of the photospheric field above latitude 55¿ is of order 10 G around sunspot minimum. ¿ American Geophysical Union 1988