Lower Ruger Mini-14 Scope Rings?

[mastiffhound]

I want to mount a 4-12x40 Vortex on my Mini for my niece and would like for it to be as low as possible. What rings have any of you tried that actually worked and are lower than the stock rings that come with the Mini? As always, thanks for your help.

 

[AKMtnRunner]

I have a Weaver 1-3x20 and Ruger #4 rings (included rings were #5). There's about 1/8-1/4" gap between top of rear ghost ring sight and scope tube. Could go even lower with #3 rings if the rear sight is taken off.