Recent work on pebble accretion in turbulent protoplanetary disks has found indications of a regime of particularly rapid growth for small planetesimals. This method of growth is possible only for a limited range of accreting body sizes, which vary with planetesimal size. When this regime is active, it would dominate growth for these planetesimals and result in layered accretion, in which a planetesimal principally accretes a particular size of body. This size decreases as the planetesimal grows, giving the planetesimal a layered structure. The upcoming NASA and JAXA missions OSIRIS-REx and Hayabusa2 will measure the size distribution of solids on the surface of asteroids, providing a direct test of this predicted layered structure. In this work, I examine this growth regime in more detail and at smaller planetesimal masses than previous studies. This allows us to determine the efficiency of pebble accretion for early planetesimals.