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Low noise CCDs fully-depleted up to 675 micrometers have been identified as a unique tool for Dark Matter searches and low energy neutrino physics. The charge collection efficiency (CCE) for these detectors is a critical parameter for the performance of future experiments. We present here a new technique to characterize CCE in back-illuminated CCDs based on soft X-rays. This technique is used to characterize two different detector designs. The results demonstrate the importance of the backside processing for detection near threshold, showing that a recombination layer of a few microns significantly distorts the low energy spectrum. The studies demonstrate that the region of partial charge collection can be reduced to less than 1 micrometer thickness with adequate backside processing.