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A new lossless data compression technique called compression by substring enumeration (CSE) has recently been introduced. CSE is competitive but it achieves lower performance on non-text-like data. More recent work confirmed that CSE incurs a penalty due to the fact that it is unaware of the position (or phase) of the bits relative to the byte boundaries. That work demonstrated that CSE can be boosted by adding a preprocessing step in which synchronization bits are inserted in the data. Various synchronization schemes were used and, in general, it has been observed that the more we insert bits, the more we improve the compression, with the best results obtained using a reliable scheme that inserts 5 bits per byte (n = 13). In this work, the authors measure the boost when using even stronger schemes. The results are negative: the use of stronger schemes (n <; 13) brings only minimal improvements.