Interplanetary shocks propagating into the magnetosphere can have significant space weather consequences. However, for many purposes it is the ejecta behind the shock that is the greater threat. The ejecta can be fast moving, impart significant momentum upon the magnetopause, and may contain a flux rope with strong southward magnetic fields. When transient solar wind activity strikes the magnetosphere, it can lead to enhanced magnetospheric currents and elevated radiation levels in the near-Earth environment. It is therefore desirable to use the observed shocks ahead of ejecta to predict any aspects of the approaching ejecta that can be predicted. We have examined 39 shocks observed by the Advanced Composition Explorer spacecraft in the years 1998 to 2003. Within the selection are shocks that were chosen because they appear to propagate significantly more slowly than the speed of the ejecta behind it. While appearing at first to be a contradiction, we show that the shocks are propagating across the radial direction and at significant angles to the velocity of the ejecta. These slow-moving shocks are actually precursors of fast-moving and potentially significant ejecta. Reversing the analysis, we are able to predict the peak speed of the ejecta well in advance of their observation, up to or in excess of 10 h following the shock crossing, when slow-moving shocks are seen, and we have incorporated this feature into our real-time shock analysis.