This paper presents a lightweight method for unsupervised extraction of paraphrases from arbitrary textual Web documents. The method differs from previous approaches to paraphrase acquisition in that 1) it removes the assumptions on the quality of the input data, by using inherently noisy, unreliable Web documents rather than clean, trustworthy, properly formatted documents; and 2) it does not require any explicit clue indicating which documents are likely to encode parallel paraphrases, as they report on the same events or describe the same stories. Large sets of paraphrases are collected through exhaustive pairwise alignment of small needles, i.e., sentence fragments, across a haystack of Web document sentences. The paper describes experiments on a set of about one billion Web documents, and evaluates the extracted paraphrases in a natural-language Web search application.