We have recently shown that efficient polymer solar cells can be fabricated by using a weakly soluble derivative of poly-p-vinylene (M3EH-PPV) as the electron donor. Here we present studies on bilayer devices using organic electron acceptors with varying LUMO levels and M3EH-PPV. It is found that the open-circuit voltage scales linearly with the LUMO level of the acceptor, reaching values as high as 1.5 V when cyano-substituted poly(p-phenyleneethynylene)-alt-poly(p-phenylenevinylene) copolymers are used. Further, we discovered that for an increasing number of triple bonds in the repeat unit of the acceptor polymer the device performance decreases with increasing thickness of the acceptor layer. Also, the quantum efficiency was smaller when using polymers with higher LUMO levels. Thus, further effort is needed to design optimum acceptor polymers for devices exhibiting large open-circuit voltage and high quantum efficiency.