Mipmap banding when using normal maps

The problem is this:


The geometry here is basic plane. I have cranked up the normals for this image for the bands to be clearly visible on a static image, but even faint ones are bad enough when you see them travel across the landscape along with the player’s movement.
The more pronounced normals i use, the more visible these bands become. They are always rendered at certain distance from the camera/player, more or less visible from different angles.
Disabling mipmaps gets rid of this problem, but all textures become a pixellated mess, so it’s not really a solution.

Texture file format is uncompressed TGA, but I doubt that it matters.
Using Blender 2.71 on Win XP. GeForce 9500 graphics card.

Hours of searching yielded a single thread from a few years back, with no answer. It’s quite a showstopper, so I’m surprised by that.