Titchy vegetables can be difficult, or even impossible, to peel correctly – let alone the New Wisdom which tells us not to peel to take best advantage of the nutrients available.
We used to peel veg in order to ensure they were thoroughly cleaned of the animal excrement used as fertiliser; this is less of a problem now. So instead of peeling try soaking your vegetables in cold water for a few minutes and then washing them using a washing up sponge (‘A bit of green’, as my mother used to call it). You may want to keep one just for this purpose; you can also use a washing up brush, or even a nail brush, to the same effect.
A bit of green also works wonders when you have a rack of lamb where you want to scrape the bones clean to impress your visitors/chef.