Spatial walk-off can severely increase the threshold of critical phase-matched optical parametric oscillations (OPOs) and distort the output beam quality. With 16-layer KTP stacks for walk-off compensation, noncritical phase-match-like (NCPM-like) and quasi-phase-match-like OPOs with enhanced angular acceptance have been demonstrated based on two different KTP bonding orientations. In the NCPM-like composite, output pulse energy of 49 microJ has been achieved at pump energy of 523 microJ with pulse duration of 15 ns and repetition rate of 1 KHz. The OPO threshold as low as 254 microJ(44.6 MW/cm(2)) has been achieved.