In online threads about Photoshop, the phenomenon is known as "banding".
one such way to disguise is to add a noise-filter, which can wholesale 'buff' out the gradient transition issue.

If there was a grain/noise filter that could be optionally applied to the bloom, say in the ADVANCED settings, it could perhaps give us better gradient blending for the HDR Bloom when used against a monochrome background, such as black.  If there were an option to control the degree of noise (either darkness, resolution, etc.) This would be very interesting as it could artistically be used for simulating dust, say in a lighted bloom area.  

Here are 2 examples, a before and after:

.iClone 7.2 Render - Bloom Rings visible


Photoshop noise filter added - Bloom Rings are 'buffed' out.  If I added more I could likewise buff out further.



Incoming message alert:
-ADD A NOISE FILTER OPTION TO THE NEW HDR BLOOM ADVANCED SETTINGS....
-NOW

PS -
100 iClone Coins to the party that gets this done.

Tony - Very nice - The artifacting in the glow is clearly eliminated. Nice job, thanks, keep those cards & letters coming!  ~V~ 

       Val RogueAnanda

RL - it could be called a "Bloom Texture", where more than just say selecting a grain/filter amount, you could have the UI allow the option to add/select an image for a Bloom filter. 
You could give the user several presets, but then the user could add in any image of their own too....  
Could potentially be an interesting added art tool element