In this paper, we present lossy off-line data compression techniques by textual substitution in which the patterns used in compression are chosen among the extensible motifs that are found to recur in the textstring with a minimum pre-specified frequency. Motif discovery and motif-driven parses of various kinds have been previously introduced and used in [5]. Whereas the motifs considered in those studies are "rigid", here we assume that each sequence of gaps present in a motif comes endowed with some individually prescribed degree of elasticity, whereby a same pattern may be stretched to fit segments of the source that match all the solid characters but are otherwise of different lengths. This is expected to save on the size of the codebook, and hence to improve compression.