I'm working on a lamp scene following a tutorial (kind of like the Pixar intro). However, I've noticed a problem with the lighting. I have a large weak light (plane) that lights the scene, but when I have it active the light from the lamp object doesn't show up on the background plane hardly at all, unless I really crank up the samples (I've gone up to 4000 and it still looks not great).
Pictures for reference (rendered with 100 samples): Here the lamp is the only light source.
Here the secondary light source is also rendered. As you can see, this makes the light from the lamp really grainy... hardly even visible.
I understand that it's harder to compute for multiple light sources, but in the past I haven't had these problems with Cycles. Then again I've never had to use such a harsh light. Is there any way I can fix this?