A theoretical analysis and an experimental study are presented on the phase-matching condition of noncollinearly pumped optical parametric oscillators (OPO's) based on a noncritical phase-matching potassium titanyl phosphate (KTP) OPO. It is shown that noncollinearly pumped, double-pass, singly resonant optical parametric oscillators maintain the advantage of round-trip parametric gain in a collinear pump, since in this case the two generated signal waves are coherent, which results in high conversion efficiency and low pump threshold. With this KTP OPO we achieved 31% energy conversion efficiency from a 1064-nm pump wave to 1572-nm eye-safe output. In addition, because the incident pump beam is not perpendicular to the OPO cavity mirrors and consequently no reflected beam flows back into the pump source, we can avoid employing optical isolators.