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The Davey-MacKay construction is a deletion-insertion correcting code scheme consisting of an inner code that functions as a pilot sequence to which the receiver seeks to synchronize, and an outer code that provides error protection. We analyse the performance of the inner code in isolation, arguing that these codes provide unequal protection, and demonstrate empirically that the error rate is dependent on the date symbol values. We also propose modifications to the code construction that alleviate this asymmetry. Simulation results show that these codes have an improved performance with no penalty.