We saw a rat in our duck enclosure! OH saw it scutter under the duckhouse. We moved it, only to find lots of little rat holes, rat poos and old bits of food. Ewwww!

We promptly dug out the tunnels (didn't find any rats though) to about a foot, and have started a strict regime of feeding the hens (next to the ducks enclosure) and ducks their ration over two feeds, so that there is not a single pellet left during the day or at night. We are also being very careful with cleaning them out and raking up debris.
But what else can we do? This is a major problem, because our landlady is massively phobic about rats and I really don't want to stress her out over it. Also, I can see they have tried to gnaw their way into the duckhouse (but haven't made it...yet).
I looked at some rat poison the other day in a DIY shop. It says that it only works if they eat it twice, and can take up to 14 days to die. Now I know this is a bit soft, but I really don't want to have rats rolling around in agony for two weeks, even if they are rats. My dad says the poison works by causing them to bleed internally

This may be a contradiction in terms, but does anyone know of any humane rat traps? or other ways I can persuade Roland and his mates to do one?