This is why I don't own a paring knife. A swivel peeler peels much more easily, evenly and waaaaay faster. For any actual cutting my utility knife does just fine.
Of the two forms shown, I very greatly prefer the Y shaped draw knife form. It is much less fatiguing and more natural to hold than the traditional knife form. Most manufacturers now make both forms.
The photo specimen is "Titan" brand. This is by far the best peeler I've ever owned, but this brand got a horrible review in Popular Mechanics, based entirely price. They used a "late night TV show" price with shipping, and I agree it was high. I bought mine at BB&B (Bed Bath and Beyond) paired with the Julienne peeler (see below). The pair cost me US $14, and I consider that a bargain, given the quality.
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Julienne Swivel Peeler
This device is very similar to a regular swivel peeler, except it has a row if vertical blades just behind the cutting blade which cut the "peel" into thin strips. This can be a fabulous time saver. You can use the thin strips as is or cut them crosswise for a very even chopped effect.
Use a regular swivel peeler to take off the skin. Then use the julienne peeler to shave the item down to nothing but shreds.
The photo specimen is "Titan" brand (see above for details). I also own an Oxo, a totally frustrating device of which Oxo should be thoroughly ashamed - it doesn't cut all the way through, so the strands don't separate. You have to pull each one from the others by hand. Yes, I checked that all the teeth were properly aligned. I also don't know what moron at Oxo thinks black is a proper color for kitchen equipment, but I see most of their stuff only in black these days.
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