> For those who don't wear a veil how often have you gotten stung in or near the eyes? 

There are other solutions, like safety glasses, including the type that fully enclose the eye region.  

I find that carefully looking at brood through a veil can be difficult, and now wear reading glasses for inspections on dull days.  Any type of glasses will prevent a direct hit from a bee flying up, but not a sting from bees getting in behind them.

We had a worker stung in the eyeball, dead centre.  The doctor in emergency removed the sting and the guy is just fine.  

Now that I don't have the high immunity I had when working with bees all season, I find stings near the eye uncomfortable, even if the swelling is minimal, so avoid them, but even then find wearing a veil a bigger discomfort most of the time., so I do get stung there sometimes  

I find that usually the bees warn me long before they start stinging and when I get stung around the eyes, it is because i overstayed my welcome by a few minutes, trying to finish something, rather than listening to my hosts.

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