How do you make the graininess go away in low-light photography?

[Elise]

I have a Olympus E-300 digital SLR. I took some pictures of my friends baby the other day while she was sleeping by lamplight. I just made the exposures longer and used a tripod rather than use a flash. They looked GORGEOUS, the lighting looked really pretty and dramatic.. but theirs a bit of graininess to the pictures, and it's quite tedious to work out with photoshop. Is there a way to avoid this, short of using the flash next time?

[Atom74]

I wouldn't use a flash, just more source light. You can always add shade and depth digitally, but not more pixels. It's the same in motion pictures, shooting day for night. They shoot in what looks like a normal daylight exposure and force it to darker in post. Also choice of exposure is critical as well.

[Dennis S]

I all most bet your using film speed of ASA 400 That's a "No -No" People use this film as the norm, and it's OK for low lighting and flash's pictures, but not for what your trying to do.
As you are using a tripod and your subject is sleeping a slower film speed is what you need, say 50, 64, 100 ASA.