I find since I have had this road bike, I often am not really sure what gear I am in!!
I can't remember if you said it was a compact double or a triple, I have been looking at gearing on compacts I could gear a 52x36 with 13-30 on the rear (providing I can get on or make one)) the same range 31.56" to 105.2" as my set up, if a 50x34 with 12-28 on the rear making it slightly higher geared than the 36x52 13-30 combination.
My current setup
A 50x34 with a possible cassette of 12-28
A 52x36 with 13-30
As you can see the 52x36 would be slightly better for me than a 50x34, also keeping that one tooth, but even so I would be working toward the high end of the cassette, and likewise on the 50 ring though better its still bigger gaps.
the numbers in purple are the gear " difference between the higher and lower gear, the % is the change in gears and the numbers on the right are the front teeth difference between small and large ring (top) the difference between low and high on the cassette (middle) and the bottom is the range the R.D. has to manage.
If you exclude the outer two cogs opposites depending high or low on the front a double compact really isn't suitable for how I ride. I would be for ever changing the front, where as I have a really usable range on the 42th middle from 44.18" to 84.97" covering almost everything I need bar the stepper climbs and descents, I spin out on the 52x13 above about 33mph but thats only down hill.
So to me a triple is a far better option, it just it doesn't come in many options on a ten sp as a new bike.
EDIT
The puncture was a pinch puncture, so the tyres haven't been breached yet.