The Born Inversions are a set of techniques for reconstructing the shape of a flaw based on the scattering of ultrasound from the flaw. One technique is the one-dimensional Born Inversion, which estimates the radius of a flaw in one direction based on one pulse-echo (i.e., backscattering) measurement in that direction. The robustness of this technique with respect to limitations on the available bandwidth and with respect to the presence of noise in the data have been investigated. The Born Inversion requires a bandwidth sufficient to include at least the range 0.5 < ka < 2 to give accurate estimates. The estimates continue to be accurate even when the amount of noise energy is comparable to the amount of flaw signal energy in the measurement.