Compress-forward (CF) relays can improve communication rates even when the relay cannot decode the source signal. Efficient implementation of CF is a topic of contemporary interest, in part because of its potential impact on wireless technologies such as cloud-RAN. There exists a gap between the performance of CF implementations in the high spectral efficiency regime and the corresponding information theoretic achievable rates. We begin by re-framing a dilemma causing this gap, and propose an approach for its mitigation. We utilize trellis coded quantization (TCQ) at the relay together with multi-level coding at the source and relay, in a manner that facilitates the calculation of bit LLRs at the destination for joint decoding. The contributions of this work include designing TCQ for end-to-end relay performance, since a distortion-minimizing TCQ is suboptimum. The reported improvements include a 1dB gain over prior results for PSK modulation.