Thin films of fully conjugated donor-acceptor block copolymers composed of an electron donating block and an electron accepting block can be used as single component photoactive layers in organic photovoltaic (OPV) devices. In order to realize their full potential, control over microphase separation and thin-film morphology are critical. In conjugated block copolymer systems where one or more blocks can crystallize, the morphological evolution is governed by the competition between microphase separation and crystallization. In this work, we control crystallization of fully conjugated block copolymers with a random copolymer block. We suppress the crystal packing of poly(3-hexylthiophene-2,5-diyl) (P3HT) through the insertion of a small number of 3-octylthiophene (3OT) units within the chains, yielding poly(3-hexylthiophene-2,5-diyl-random-3-octylthiophene-2,5-diyl) (P[3HT-r-3OT]). While crystallization of P3HT dominates the morphology and prevents microphase separation in poly(3-hexylthiophene-2,5-diyl)-block-poly((9,9-dioctylfluorene-2,7-diyl)-alt-(4,7-di(thiophene-2-yl)-2,1,3-benzothiadiazole)-5′,5″-diyl) (P3HT-b-PFTBT), modest levels of 3OT suppress crystallization in P[3HT-r-3OT]-b-PFTBT, and permit microphase separation. Thus, we demonstrate that incorporating a random copolymer into a donor-acceptor block copolymer can increase control over microphase separation and lead to enhanced performance in OPV devices.