Call heard only at dawn or dusk

The call of this mystery bird kind of sounds like COO-Wee. The COOO is held for a little longer than the WE. The WE is cut short. So a bit like this: Cooooo-We.

I am having a hard time actually sighting this bird. I only hear it very early in the morning, just on day break, and again at dusk. I saw it just once early one morning sitting high up in a neighbour's tree. But since he was sitting against the rising sun, I could not discern any colours. It was about the size of a crow, with a relatively long tail and a short but slightly curved beak at the tip.

Location: Lockyer Valley, Qld.

Any ideas?