1. I draw the flowers on a simple quad. The bitmap I send to OpenGL contains no visible white.
   
2. I use mipmaps with GL_NEAREST_MIPMAP_NEAREST.
   
3. The bitmap is of the format GL_RGBA8. The alpha channel is either 0 or 255 (yes, I will probably switch to GL_RGB5_A1).
   
4. The fragment shader doesn't use blending, it uses the alpha to discard pixels.
   
5. I use GL_CLAMP_TO_EDGE for S and T.
   
6. The color of the transparent areas are pure white (Photoshop makes it that way). I think some of this white is bleeding through. Although, a little bit of the line is black sometimes (flickering depending when turning camera).
   
7. If I don't use mipmaps, the problem goes away.
   

may be problem in texture?
are you sure that all white pixels with alpha less in you discard value in fragment shader?

When your mipmaps are created the mipmap pixels are set to the average of several pixels in the larger mip-levels, ...

OpenGL uses averaging when creating mipmaps.

[background=rgb(250, 251, 252)]GL_NEAREST_MIPMAP_NEAREST controls how the mipmap is used, not how it is created. I also found, as could be expected, that using 0.5 as threshold for the alpha made some pixels go away that shouldn't. In that case, the problem was the other way around.[/background]

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The problem is that I get alpha values between 0 and 1, but I have a pixel culling algorithm in the fragment shader that depends on the alpha being either 0 or 1.

I am not sure if this design can be combined with the use of mipmaps?

You can create the mipmaps manually

Today, I am simply using glGenerateMipmap(GL_TEXTURE_2D);