Words unknown to the lexicon present a substantial problem to part-of-speech tagging. In this paper we present a technique for fully unsupervised acquisition of rules which guess possible parts of speech for unknown words. This technique does not require specially prepared training data, and uses instead the lexicon supplied with a tagger and word frequencies collected from a raw corpus. Three complimentary sets of word-guessing rules are statistically induced: prefix morphological rules, suffix morphological rules and ending guessing rules. The acquisition process is strongly associated with guessing-rule evaluation methodology which is solely dedicated to the performance of part-of-speech guessers. Using the proposed technique a guessing-rule induction experiment was performed on the Brown Corpus data and rule-sets, with a highly competitive performance, were produced and compared with the state-of-the-art. To evaluate the impact of the word-guessing component on the overall tagging performance, it was integrated into a stochastic and a rule-based tagger and applied to texts with unknown words.