I'm assuming you are working with the images that were discussed in the context of the DeleteBorderComponents question. I'm not able to reproduce the problem you see. For example, using the attached binary image obtained via:
im = Import["jqa_v12_p01.jpg"]
binary = MorphologicalBinarize[ColorNegate[im]]
If I call DeleteSmallComponents with a small threshold, like 300, you can see that lots of the little speckle components are deleted.
DeleteSmallComponents[binary, 300];
ImageDifference[binary, %]
If I ramp the component size threshold way up, the result is a blank black image since every component is deleted.
DeleteSmallComponents[binary,10000000]
Does that help?
Attachments: