Bit-interleaved coded modulation (BICM) is often the method of choice for multilevel transmission over fading channels. If relatively simple forward error-correction (FEC) codes such as convolutional codes are employed, iterative decoding between demapper and FEC decoder can provide significant performance improvements over non-iterative decoding. To keep the complexity of iterative decoding low, the use of hard-decision feedback from FEC decoder to demapper is appealing. However, the price to be paid is a performance degradation due to feedback errors. In this letter, two new demapper designs are developed which are able to strongly mitigate the effect of erroneous feedback. The key ideas are (a) the use of an estimate of the average error rate for the hard-decision feedback and (b) the interpretation of feedback errors as additive impulsive noise. Simulation results show that the proposed designs achieve error rates close to those for iterative decoding with soft feedback, while they maintain the complexity advantage of using hard decision feedback.