No - mine is without the thumb break - just the strap.
This is for the times when I feel I will need my handgun the least - when I calculate the odds are against me needing it immediately -like when I am at work. I work less than a mile from my home - in a very rural area - in a non-commercial office that keeps no money on site - so its not like being in a big city walking through dark alley ways holding a bag of cash - if you catch my drift.
When I calculate the odds are greater that I will need my handgun - like when I go to town - I carry in a more easily accessible mode.
I know some are of the opinion to always carry in the same exact place all the time - and for some that is probably good advice - but I practice drawing from every mode of carry I use - and I know my body "knows" where my handgun is on my body - in other words my body is VERY aware of where my handgun is no matter what mode of carry I happen to be using at that time.
Hope this helps,
cheers
tire iron