RE: Thick cover compact binoc' s...what do you use/recommend?
The discussion of optics is about like the argument between Momentum and Kinetic Energy. Of course Zeiss, Nikon, Swarovski names are well worth owning but they are not the only good optics available.
By the best you can afford; it is as simple as that.
I use a pair of compact Minolta [at $300.00+] in 8X22X8.2 and I have had owners of more expensive named units say that mine are GREAT. They are lite, fit into a pocket and share time with my Bushnell Laser Rangefinder; but they also have their limitations. If I had only the larger units, I simply would not carry them because of weight. I hunt on foot far off roads and trails and weight is definitely a factor.