  We report on 49 fast-mode forward shocks propagating inside coronal mass
ejections (CMEs) as measured by Wind and ACE at 1 AU from 1997 to 2006.
Compared to typical CME-driven shocks, these shocks propagate in different
upstream conditions, where the median upstream Alfv{\'e}n speed is 85 km
s$^{-1}$, the proton $\beta = 0.08$ and the magnetic field strength is 8 nT.
These shocks are fast with a median speed of 590 km s$^{-1}$ but weak with a
median Alfv{\'e}nic Mach number of 1.9. They typically compress the magnetic
field and density by a factor of 2-3. The most extreme upstream conditions
found were a fast magnetosonic speed of 230 km s$^{-1}$, a plasma $\beta$ of
0.02, upstream solar wind speed of 740 km s$^{-1}$ and density of 0.5
cm$^{-3}$. Nineteen of these complex events were associated with an intense
geomagnetic storm (peak Dst under $-100$ nT) within 12 hours of the shock
detection at Wind, and fifteen were associated with a drop of the storm-time
Dst index of more than 50 nT between 3 and 9 hours after shock detection. We
also compare them to a sample of 45 shocks propagating in more typical upstream
conditions. We show the average property of these shocks through a superposed
epoch analysis, and we present some analytical considerations regarding the
compression ratios of shocks in low $\beta$ regimes. As most of these shocks
are measured in the back half of a CME, we conclude that about half the shocks
may not remain fast-mode shocks as they propagate through an entire CME due to
the large upstream and magnetosonic speeds.
