We identify 10—seven for the first time—elements of cold halo substructure (ECHOS) in the volume within 17.5 kpc of the Sun in the inner halo of the Milky Way. Our result is based on the observed spatial and radial velocity distribution of metal-poor main-sequence turnoff (MPMSTO) stars in 137 Sloan Extension for Galactic Understanding and Exploration lines of sight. We point out that the observed radial velocity distribution is consistent with a smooth stellar component of the Milky Way's inner halo overall, but disagrees significantly at the radial velocities that correspond to our detections. We show that all of our detections are statistically significant and that we expect no false positives. These ECHOS represent the observable stellar debris of ancient merger events in the stellar accretion history of the Milky Way, and we use our detections and completeness estimates to infer a formal upper limit of 0.34+0.02 -0.02 on the fraction of the MPMSTO population in the inner halo that belong to ECHOS. Our detections and completeness calculations also suggest that there is a significant population of low fractional overdensity ECHOS in the inner halo, and we predict that 1/3 of the inner halo (by volume) harbors ECHOS with MPMSTO star number densities n ≈ 15 kpc-3. In addition, we estimate that there are of order 103 ECHOS in the entire inner halo. ECHOS are likely older than known surface brightness substructure, so our detections provide us with a direct measure of the accretion history of the Milky Way in a region and time interval that has yet to be fully explored. In concert with previous studies, our result suggests that the level of merger activity has been roughly constant over the past few Gyr and that there has been no accretion of single stellar systems more massive than a few percent of a Milky Way mass in that interval.