Compression removes redundancy. It's literally the definition of compression! And reduced redundancy is always bad when reliable transmission is a priority over small size.
Bit of a late reply, but resending it is a form of redundancy, and so is adding error correction bits. It is cheaper to do these things (they require less bandwidth) when you start with a limited character set.
Even a static huffman tree would help, and has no overhead. An entropy encoder would do very well and only cost a few bits to flush.