Far as I'm concerned, when you get aphids you only have two options. Toss out the plants or go nuclear. Soaps and organic solutions are not going to phase aphids. Its time to break out broad spectrum insecticides like sevin and glaze the mofos.

Hi! LOL! Can totally understand frustration with aphids!@_@ I'm no gardening expert here, but many people recommend getting ladybugs!=) Or you can reduce their numbers greatly by shooting lots off with a garden hose first before treatment!=P Spraying with a soap solution has worked moderately well for me before, and I think I've heard people say neem...=X I don't know what Triazicide is, so I don't know how effective it is on aphids.=/

But the thing with aphids is that they reproduce sooo quickly by parthenogenesis, that all you really need is one little aphid to land on your plant to get lots of trouble!=/ They make me wanna rip my hair out sometimes! I try to squish them by hand, and I'd think I got them all, then the next day it'd look like I'd done nothing at all...=(

I second the motion brought forth by Edymnion. I had a TON of them last winter. I tried soap and I tried washing them off and I tried to go organic with it. The aphids laughed at me and could have made a great Allstate Mayhem commercial. I hammered those bastards with sevin and they were all dead within a week. My overwintered peppers survived. If you do not want to get nuclear with the pesticide...my advice is that its not worth dealing with....they are incorrigible.
Good luck....I hate APHIDS!

I only overwinter a few plants each year. But, I've had good luck with store bought insecticidal soap. If you have to use too much, it may be too expensive. The thing is most "dish soaps" are not soaps, but, detergent. I don't know specifically about the product you used.

Edymnion: I love the Nuclear Sevin shots every time someone has a pest problem. I laugh every time. However, I used insectidal soap last fall and it worked. Not as easy or quick as a tactical Sevin Nuclear warhead but it worked. Nuke was my next option.

I am battling fungus gnats now and using Hydro peroxide to start. If that doesn't work, I have a Sevin warhead armed and on the launch pad.
Bruce

Okay, lol, my bad, I forgot to mention that the soap I used was insecticidal soap that came in a green bottle with a picture of aphids, spider mites, and mealy bugs on it!=P Then I squirted everywhere, especially the undersides of leaves!=) So far that has worked okay for me, but I do find that I need to reapply a few times to make sure I got rid of them. I hate aphids, but currently I have a plant with spider mites, so I hate them even more right now!=/

Oh! Almost forgot, I once made a diluted garlic oil solution I found on the internet that was working well(just in case someone is looking for an insecticide alternative), but I don't know if it'll get rid of them completely, because I changed to the soap halfway, cause my mom bought a bottle. Basically I minced some garlic, soaked it in oil for many hours, then diluted it a lot before spraying. But you have to make sure to test on a small area of your plant beforehand, so you know it doesn't harm your plant or anything!=)

Well Bruce, I'm of the opinion that organic solutions are fine for mild to moderate problems. Once it moves beyond "I saw a caterpillar eating a leaf" and into "the bugs have cocooned my plant are beginning to erect barricades and set up little pots of boiling oil to repel invaders", its time to drop the bomb.

Edy: You ever consider trying sanctions first? I am with you, talks and negotiations don't work. Arm the warheads.
Bruce

Yeah, I guess I shouldve just used Sevin, but the last time I used it was when Lawn Doctor tried to save $$ by switching to "Sevimol"(Sevin + molasses)(LOL!).... Lets just say it didnt work well, and it was a liquid, which ended up blowing back onto our boots and pants, so we spent the rest of those work days all sticky and smelling like molasses! What a joke!

Then we switched to Dylox as a curative grub control. It was that experience in 1991 that has soured my opinion of Sevin, but maybe it works well with other insects, and compared with other insect controls, it's relatively safe, and listed for use on edible plants so......... Malathion is an option, but it smells nasty!

Yah, if the stuff has all kinds of warnings on it, it is probably pretty effective at stopping critters. Careful is the word.

I know back in the 70's, my Mom used to use Chlorine Dust for anything from ants to slugs to spiders, whatever. It always worked without fail. But that was outlawed many years ago. She was overjoyed when i was able to pick up a can of it for $1 at an auction last summer. I suppose it is second cousin to DDT and why it was outlawed, but it was effective.
Bruce

Yup, I just get the sevin premixed spray. The trick is to be careful when and how you use it. Luckily in my experience the stuff that really likes to eat my plants don't come out at the same time as the things that like to pollinate my plants.

If your peppers are anywhere close to having flowers (as in, they already have the little hanging lantern flower buds starting to form), then I try whatever else I can first. Don't want broad spectrum insecticides on your plants at the same time as flowers, or you're just going to kill your bees and other pollinators.

Luckily though, by the time the pollinators are active, so are the ladybugs and parasitic wasps and all the other natural controllers, so you don't have to spray except in rare cases.

Heh, I probably have a reputation for all my plants having a permanent white glaze on them from how fast I am to say to hit the sevin, but I really don't use that much of it. Its just that usually by the time people make a thread its already reached panic time.

Tapla has a great post in insects in the pest forum.