We report on 49 fast-mode forward shocks propagating inside coronal mass ejections (CMEs) as measured byWind 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 Alfvén speed is 85 kms−1, the proton 훽 = 0.08 and the magnetic field strength is 8 nT. These shocks are fast with a median speed of 590 kms−1 but weak with a median AlfvénicMach number of 1.9. They typically compress the magnetic field and density by a factor of 2–3. The most extreme upstream conditions foundwere a fast magnetosonic speed of 230 kms−1, a plasma 훽 of 0.02, upstream solar wind speed of 740 kms−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 h of the shock detection atWind, and 15 were associated with a drop of the storm time Dst index of more than 50 nT between 3 and 9 h 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 훽 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.