Chances are she's waking up because she's just about to drift off - happens to DS and me too. Something just jars you out of sleep. Have you tried the pat-and-shush route until she's asleep again?

You say you put her down when she's tired. Where? In her cot in a room alone? With you? In a pushchair? Could where you're putting her be waking her? - maybe she's lonely without you, or maybe she's cold in another room, or the radio wakes her.

The other advice is that babies don't get the whole sleep-is-important thing and we just have to live with it until they do get the idea. Saved my sanity a few times in the last 9 months!