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Current ASR and MT systems do not operate on conversational Finnish, because training data for colloquial Finnish has not been available. Although speech recognition performance on literary Finnish is already quite good, those systems have very poor baseline performance in conversational speech. Text data for relevant vocabulary and language models can be collected from the Internet, but web data is very noisy and most of it is not helpful for learning good models. Finnish language is highly agglutinative, and written phonetically. Even phonetic reductions and sandhi are often written down in informal discussions. This increases vocabulary size dramatically and causes word-based selection methods to fail. Our selection method explicitly optimizes the perplexity of a subword language model on the development data, and requires only very limited amount of speech transcripts as development data. The language models have been evaluated for speech recognition using a new data set consisting of generic colloquial Finnish.