Segment highly packed nuclei with dotted high intensity signal inside each object
I wouldn't bother with correct bright pixel segmentation.
I think such a strategy would add complexity and another stage in the algorithm which might add errors at the eventual product.

I would use some form of scaling function for the pixel value so that the bright pixels would blend-in better while maintaining contrast in the darker pixels. One such function could be the log function:


  im = log(double(im));




Another one might be the square root.
You might even get away with using a max value for the image , e.g. 


  thr = 150; im(im> thr) = thr;


or a combination of both, for instance a capped transform function
thr = 100; 
tform_im = img.^0.5;
tform_im_scaled = tform_im - min(tform_im(img>thr)) + thr;
img(img>thr) = tform_im_scaled(img>thr);

 

Either way good luck!