We report on an improvement of idler beam quality in a singly resonant optical parametric oscillator (OPO), where the resonant signal is converted to the idler via an additional difference frequency generation (DFG) process. The two processes are phase matched simultaneously by a quasi-periodically poled nonlinear crystal. Whereas back-conversion of the signal and idler to the pump frequency distorts the idler beam in a standard OPO, in a quasi-periodic OPO the DFG process reduces the signal intensity, leading to suppression of back-conversion and, hence, improvement in idler beam quality. Indeed, the experimental results show under the same pump power a significant improvement in idler beam quality for the quasi-periodic OPO (1≤M2≤2.1) as compared with the standard OPO (3.2≤M2≤5.3).