We consider gapped variants of classical data compression paradigms by Ziv, Lempel, and Welch. In the original algorithm, phrases are identified and stored in a dictionary on-the-fly as the textfile is scanned. The entries in the dictionary are then matched against the incoming string, thereby determining the next codeword, and this gives the method an inherently linear-time implementation. In our variants, the phrases used in compression are selected among suitably chosen strings of intermittently solid and wild characters produced by the autocorrelation of the sourcestring, in a way that still preserves linearity of time. At the receiver, gaps can be filled back exactly, interpolated, or left blank, so that lossless as well as lossy implementations are possible. However, the focus of this paper is on lossy variants.