Generally you will have to trade off the two effects. The goal should be lots of noise reduction with minimal disturbance to the 'real' curve. But the only way to take out the noise without changing the 'real' curve is if you already know what the real curve looks like, in which case you don't need to de-noise corrupted data in the first place.
Well, for Gaussian noise, the correlation properties completely characterize it. I.e., there aren't any other independent noise properties. The key will be using assumptions on how the "real" data should behave: smoothness, correlation, monotonicity, something along those lines. The way to proceed is to figure out exactly what you DO know about the data (which is presumably less than exactly what the real curve looks like), and then apply that. But for anyone to help, you'll first have to tell us what you already know about the data.