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Perpendicular writing fields are calculated for finite pole-length gapped heads, with and without a permeable layer beneath the magnetic medium. These head fields are used to compute readback waveforms from ideal perpendicular transitions, which are detected both by zero-crossings and by inflection points of the waveform. Linear readback bit shift, given by the difference between detected and written transitions, is normalized to half the minimum transition spacing. For detection by waveform zero-crossing, bit shifts are unacceptably large with an under layer. Without an underlayer, detection by inflection point is considerably better than by waveform zero-crossing. Surprisingly, bit shifts from inflection points are only marginally better without an underlayer than with one. A recording system with an underlayer may in fact give superior performance because of other contributions to the total bit shift.