We have revealed a substantial enhancement of third-order optical figure of merits by the synthesis of a compact molecule possessing the tetrathiafulvalene (TTF) group with two backside C=O groups. Addition of the saturated methylene chain substantially suppresses the third-order optical figure of merits and even local optical hyperpolarizabilities at lambda = 532 nm. Another TTF-derivative molecule possessing ethylenic and acetylenic chains demonstrates large hyperpolarizabilities; however, generally, the figure of merit factor decreases due to the increasing optical losses as a consequence of enhanced linear absorption. At the same time, both of the chromophores have a large nonlinear optical response. General approaches for search and design of the third-order optical materials with improved properties are given.