We present arguments regarding diquarks possible role in low-energy hadron phenomenology that escaped theorists' attention so far. Good diquarks, i.e. the 0^+ states of two quarks, are argued to have a two-component structure with one of the components peaking at distances several times shorter than a typical hadron size (a short-range core). This can play a role in solving two old puzzles of the 't Hooft 1/N expansion: strong quark mass dependence of the vacuum energy density and strong

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... ons of the Okubo-Zweig-Iizuka (OZI) rule in the quark-antiquark 0^± channels. In both cases empiric data defy 't Hooft's 1/N suppression. If good diquarks play a role at an intermediate energy scale they ruin 't Hoofts planarity because of their mixed-flavor composition. This new scale associated with the good diquarks may be related to a numerically large scale discovered in [V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B 191, 301 (1981)] in a number of phenomena mostly related to vacuum quantum numbers and 0^± glueball channels. If SU(3)_ color of bona fide QCD is replaced by SU(2)_ color, diquarks become well-defined gauge invariant objects. Moreover, there is an exact symmetry relating them to pions. In this limit predictions regarding good diquarks are iron-clad. If passage from SU(2)_ color to SU(3)_ color does not lead to dramatic disturbances, these predictions remain qualitatively valid in bona fide QCD.