Cochran, Orr, and Teichner introduced the n-solvable filtration of the knot concordance group, which has given a framework for recent advances in the study of knot concordance. However, it fails to detect anything about topologically slice knots, denoted T. We define a new filtration of the knot concordance group, relate it to known concordance invariants, and use Heegaard Floer homology to prove that it induces a non-trivial filtration on T. One application of this filtration is to say more about the fractal nature of the knot concordance group, i.e. the complexity of the Cochran-Orr-Teichner filtration embeds into T. This is joint work with Tim Cochran and Shelly Harvey.