Unary Error Correction (UEC) codes have recently been proposed for the near-capacity Joint Source and Channel Coding (JSCC) of symbol values that are selected from a set having an infinite cardinality. In this paper, we characterize the computational complexity of UEC decoders and use complexity analysis for striking a desirable trade-off between the contradic- tory requirements of low complexity and near-capacity operation. We investigate a wide range of application scenarios and offer a deep insight into their beneficial parameterizations. In particular, we introduce puncturing for controlling the scheme’s throughput and for facilitating fair comparisons with a Separate Source and Channel Coding (SSCC) benchmarker. The UEC scheme is found to offer almost 1.3 dB gain, when operating within 1.6 dB of the capacity bound. This is achieved without any increase in transmission energy, bandwidth, transmit duration or decoding complexity.