Video compression systems must support increasing bandwidth and data throughput at low cost and power, and can be limited by entropy coding bottlenecks. Efficiency can be greatly improved by parallelizing coding, which can be done at much larger scales with new neural-based codecs, but with some compression loss related to data organization. We analyze the bit rate overhead needed to support multiple bitstreams for concurrent decoding, and for its minimization propose a method for compressing parallel-decoding entry points, using bidirectional bitstream packing, and a new form of jointly optimizing arithmetic coding termination. It is shown that those techniques significantly lower the overhead, making it easier to reduce it to a small fraction of the average bitstream size, like, for example, less than 1% and 0.1% when the average number of bitstream bytes is respectively larger than 95 and 1,200 bytes.