Many displacive solid-solid transformations, despite being first order, show pronounced precursor effects, such as the mesoscopic, micron-scale, "tweed'' pattern seen in shape-memory alloys. We model this tweed theoretically using a nonlinear, nonlocal elastic free energy, and argue that quenched concentration inhomogeneities drive the local tweed modulations. We report (1) the construction of a model for {l l}/(lT) shear transformations in square systems, (2) a simulation including concentration inhomogeneities, and (3) a mapping of the disordered 2D martensite onto an infinite-range spin model, identifying tweed with the spin-glass phase.PACS numbers: 8I.30.Kf, 61.70.Wp, 75.10.Nr In textbook first-order phase transitions critical fluctuations are negligible: Water shows no hint of incipient solidity above 0°C. First-order solid-solid displacive transformations are strikingly different; precursors are common for tens through hundreds of degrees away from the transitions. We study here the tweed pattern [l] observed in electron micrographs well above the transition temperature in the so-called medium and weak martensites, including the shape-memory alloys FePd [2] and NiAl [3], the superconducting ^-15's [4], and high-T^ Y-Ba-Cu-Co-O, and Y-Ba-Cu-Al-O [5,6]. The tweed appears as a characteristic cross-hatched pattern. X-rayand electron-dilTraction measurements [2,3,7-10] indicate that tweed is a local mixture of undeformed and deformed regions, and that it arises from a local {llO}/