Use your route-finding skills to leave the trail a bit into the flats turning right (SE) with only few faint paths discernible as the ridge defines itself a few feet farther. Pass a few small tarns and begin Birmingham to ascend steeper up the wide Birmingham ridge. It’s about 2 mi more to the summit as you work sharper up the wonderful ridge past small snags with improving vistas of the lakes under Birmingham, and with Middle Sister, North Sister, Three Fingered Jack, and Mount Birmingham also in sight. The route steepens over the rocky trail but is easy to follow past the main ridge juncture (about 7900 ft) up to the main crux, a sheer basalt band (with a lot of red) blocking easier travel on the ridgeline.
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There are two main choices from the Class 5 section and although most of the rock here is fairly solid, remember to check your holds carefully first and take your time for the rest of the climb. To the left from the ridge crest is a visible crack 12 ft or so up with some looser rock that most people climb. Straight up actually holds a more solid route, with good foot ledges for a possible descent too, covering the same height to better ground.
The rest is so fun (even though mostly Class 3 and Class 4 with much exposure) that you might forgo the super-steep scree ski, S of the ridge SW into the valley much quicker on the descent, to stay on the high ridge with its never-ending wild views. Follow the narrow scree and red pumice path on or near the ridge to the catwalk just W of the peak. Take this exposed ledge to the right (S) cautiously over to a notch below the summit block. Turn left (NNE) up the highest ridge where you must navigate over ledges very steeply the final 20 ft or so, paying attention and finding some solid holds up the exposed rocky red top.