This paper examines spurious dianeutral transport within a suite of ocean models (GOLD, MITGCM, MOM, and ROMS). We quantify such transport through a global diagnostic that computes the reference potential energy, whose evolution arises solely through transport between density classes. Previous studies have focused on the importance of accurate tracer advection schemes in reducing the spurious transport and closure. The present study highlights complementary issues associated with momentum transport. Spurious dianeutral transport is shown to be directly proportional to the lateral grid Reynolds number (Re-Delta), with such transport significantly reduced when Re-Delta < 10.