Three passes of the ISEE 1 and 2 satellites through the dayside terrestrial magnetopause are discussed where the magnetopause is identified as a tangential discontuity. The identification is based primarily on the failure of the plasma and magnetic field data to satisfy the conditions for a rotational discontinuity. In all these cases the interplanetary magnetic field was directed strongly southward and the angles between the fields on the two sides of the magnetopause ranged between 136¿ and 170¿. As this is precisely the field geometry thought to be most conductive for reconnection, one would have expected the magnetopause to be a rotational discontinuity. The simplest explanation of this result would appear to be that the magnetic field orientation is not the only factor controlling the onset of reconnection. However, as our identification of the discontinuity applies only locally, it cannot be excluded that for the magnetic field conditions investigated here, different portions of the magnetopause can be described as tangential and rotational discontinuities simultaneously.