The majority of online content is written in languages other than English, and is most commonly encoded in UTF-8, the world's dominant Unicode character encoding. Traditional compression algorithms typically operate on individual bytes. While this approach works well for the single-byte ASCII encoding, it works poorly for UTF-8, where characters often span multiple bytes. Previous research has focused on developing Unicode compressors from scratch, which often failed to outperform established algorithms such as bzip2. We develop a technique to modify byte-based compressors to operate directly on Unicode characters, and implement variants of LZW and PPM that apply this technique. We find that our method substantially improves compression effectiveness on a UTF-8 corpus, with our PPM variant outperforming the state-of-the-art PPMII compressor. On ASCII and binary files, our variants perform similarly to the original unmodified compressors.