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The proposed method can detect changes in various different signal structures; we focus on the examples of piecewise-constant and continuous, piecewise-linear signals. The novelty of the proposed algorithm comes from the data-adaptive nature of the methodology. At each step, and for the data under consideration, we search for the most prominent change-point in a targeted neighborhood of the data sequence that contains this change-point with high probability. Using a suitably chosen contrast function, the change-point will then get detected after being isolated in an interval. The isolation feature enhances estimation accuracy, while the data-adaptive nature of DAIS is advantageous regarding, mainly, computational complexity. The methodology can be applied to both univariate and multivariate signals. 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