Given the lack of word delimiters in written Japanese, word segmentation is generally considered a crucial first step in processing Japanese texts. Typical Japanese segmentation algorithms rely either on a lexicon and syntactic analysis or on pre-segmented data; but these are labor-intensive, and the lexico-syntactic techniques are vulnerable to the unknown word problem. In contrast, we introduce a novel, more robust statistical method utilizing unsegmented training data. Despite its simplicity, the algorithm yields performance on long kanji sequences comparable to and sometimes surpassing that of state-of-the-art morphological analyzers over a variety of error metrics. The algorithm also outperforms another mostly-unsupervised statistical algorithm previously proposed for Chinese. Additionally, we present a two-level annotation scheme for Japanese to incorporate multiple segmentation granularities, and introduce two novel evaluation metrics, both based on the notion of a compatible bracket, that can account for multiple granularities simultaneously.