Bit Patterned Media (BPM) are a possible technology for use in future hard disk drives where a single nanoscale island is used to store each bit of information. However, the imperfect island fabrication process results in unavoidable variations in the geometry of the islands, which introduces deterministic changes in the replay signal and leads to errors in the conventional Maximum Likelihood (ML) detector. If the detector can be extended to include estimates of island size, then detector decisions can be improved and error rates reduced. A read channel is proposed that reduces the impact of island size variations by modifying the detector trellis to include two extra branches per state transition to improve the data error rate at the output of the detector. An analytical model of the modified read channel is developed that is capable of rapidly estimating the bit-error-rate (BER) performance so that the modified read channel trellis parameters can be optimized to maximize the BER improvement offered by the proposed detector. In order to verify the performance of the analytical model its output is compared with that produced from a numerical model, which takes full account of multi-bit inter-symbol interference.