Best Treatment for Broken Capillaries on Nose?

If the vessels you are talking about are on the nasal alae (the side of the nose where it meets the cheek and upper lip), these are arterial capillaries, and quite difficult to eradicate. The best way to eliminate them (if they are big enough to stick with a 30-gauge needle), is via sclerotherapy using 1% sotradecol, 3% Polidocanol, or hypertonic saline--this is quite uncomfortable but usually works in one session. The next best way is with a cat's whisker electrocautery--this technique can leave tiny puncture scars are the entry site for the tiny electrical wire, but usually works in one session. The only other technique (and third on the list) that I would recommend for these vessels is KTP laser, but even this technique can take more than one session, can yield slight depressions (scars) where the vessels are sealed shut, and hurts a bit also.

For these high-flow nasal ala vessels, pulsed dye laser, V-beam laser, IPL, and other laser wavelengths are basically of little value. You can "pound" these vessels with multiple sessions and high powers, but at what cost, downtime, and benefit? Why not just use a hot poker?

For the tiny capillaries elsewhere on the nasal skin (such as seen with Rosacea), these are not "broken," but they are dilated venous capillaries that respond well to pulsed dye laser, V-beam laser, or IPL if topical dermatologic medications are ineffective. Proper energies must be used, and experienced laser physicians are recommended.

For Broken Capillaries (telangiectasias) on the face there is a number of lasers that work well. Though IPL or BBL at the proper settings correct many there are also specialized laser such as the Diolite KTP laser, Sciton laser and Candella tuneable dye laser that work great for these problems. I do NOT recommend doing sclerotherapy around the nose as complications, some serious may occur in this area.

If you want to improve your skin tone, reduce spider veins or rosacea Palomar's IPL provides the most skin-safe, comfortable, and effective photofacials available, with little to no downtime. Depending on the severity of your condition, expect to get 3-5 treatments but it is worth it. You will get big improvement with the first treatment.

The best and quickest way to treat broken capillaries on or around the nose is with the VBeam Laser. VBeam is the most advanced Pulsed Dye Laser Technology, VBeam treats red skin, broken blood vessels, rosacea, and birthmarks. This laser targets the selected area with an intense yet gentle burst of light. This laser is so safe that it’s used for the treatment of port wine stains on infants and young children. It also treats photoaging and sun damage with no downtime.

These are common occurrences for men and women.They are treated with different modalities including long pulse KTP lasers. Remember that multiple treatments may be necessary as well as repeat treatments in the future. 

For problems such a broken capillaries, lasers like the Pulsed Dye or Nd: YAG work best by using light energy to home in on ruddy pigment and erasing red areas on the face and body.
When using a laser, a doctor does one pass, or several, over secions with persisten redness, The wavelength recognizes only high concentrations of pigment in the visible capilaries. Once heated, those vessels shrivel and disappear. In most cases, one to two laser sessions spaced over four to six weeks are necessary to reach complete clearance. Postprocedure, skin may be slightly irritated for a few days.

I agree with Dr. Oppenheim that you other options are the pulsed-dye laser (v-beam), KTP (q-switched 532/1064). The YAG 1064 laser is also very good for larger vascular lesions. Incidentally certain IPL devices are equipped with various filters and are more effective for vascular lesions. Another factor is whomever is treating you should be versed in troubleshooting and tinkering with settings to give you the best results. Choose your practitioner carefully.
Good luck.

The Pulsed dye laser, V Star is the one with which I am most familiar, is an excellent laser for those troublesome capillaries. The Versapulse KTP vascular laser is also a good choice.
For those on a tighter budget, electro-cautery ( the "poor man's laser" ) does just about the same thing, for a much lower cost.