Barlow's Buttress is the center crack approaching the high roofs near the right side of the Playground. The cruxes are at the beginning and end of the climb. A tricky boulder problem just off the ground lets one get a hand-size cam in a slot just at the hard part. Pull on a chockstone through the first crux. Being tall probably helps. 5.8 cracks up to the big roof (this is the next crack system to the right of Upper Left Roof, at this point). A second crux turns the highest roof to the righthand side- this is protectable with smallish nuts and some cams under the roof but is still fairly awkward. One may also be able to exit by the center roof crack up high? or avoid the upper crux entirely by traversing right a little lower- escaping to the upper section of Battle of the Bulge.
Other than the tricky start (which isn't too high off the deck), good pro the whole way. Jemez Rock calls this 5.11a. Chen/Wehner online guide sandbags us with a 5.9+ grade. I don't know what RC:NM says. (My opinion: 10ish.. it's got good pro..)
Location
This climb is the center line below the high roofs near the right side of the Playground, on the face to the right of Beginner's Hand Jam and Upper Left Roof.
Protection
1 set cams to 3", and nuts. Save some gear to build an anchor. Like most at the Playground, the climb ends on the big ledge 20' below the clifftop, so anchoring off trees is not the best option.