I set out to climb Haeckel's Northwest Arete yesterday - I have no idea now whether what I climbed was the "classic" route or not! There seems to be some confusion in the guidebooks I looked at after the fact.
Here's what I did. From Lake 12345 I climbed up the obvious snow gully to a col. This is what Secor advises - ascend to the first notch to the northwest of Haeckel. From here there are three obvious features. On the left is the prominent arete with huge towers that you can see on the approach. In the middle is a shallow, loose gully. On the right is another ridge, but not so sharp that I would call it an "arete". Thinking I was here to climb an arete, I downclimbed a bit from the col, across the gully, and tried to head up to the left. I thought it would be a good idea to bypass the first large tower since it didn't look a bit 4th class, so I worked my way up 4th class cracks. These cracks kept pushing me toward the gully though, as they steepened well beyond 4th class the closer I got to the arete. Finally I just dropped into the gully and climbed up a ways, looking for a way to jump back on the arete. I gave up this idea in short order because the arete just got steeper, with towers and needles that looked much harder than 4th class. Looking across the gully, I started thinking the other ridge might be the right on, so I headed for that one, and took it to the summit. This definitely was 4th class ground. I descended this ridge in its entirety, and found beautiful, solid 4th class climbing almost top to bottom; I would call it a classic climb myself.
Secor's guidebook shows a picture which looks like it exactly matches the ridge on climber's right, the one I downclimbed and climbed in part. Moynier and Fiddler's guidebook, on the other hand, shows a completely different route, one which looks like it leads to the left arete. I doubt this arete is 4th class, although perhaps if one is right on top of it the route can be kept 4th class. Anybody know any better than me? I think the ridge leading more or less directly from the notch is the actual NW arete, since it is definitely 4th class and struck me as a clean, high quality route.