Just right of Mystery of the Desert is a broken crack system. P1 - 5.7 climb the thin slab to reach the cracks. You will be about 20 feet up before you can place your first pro but after that you can stitch it up like an old pair of underwear. Climb to where the cracks end at a horizontal rock band and belay. We moved slightly up and left and belayed from the 2 bolt anchor. P2 - the money pitch (way fun) - move right to the right leaning weakness, step onto the right face and climb up to a band of broken rock 5.7/8. Clip the bolt and make the crux move above to get your hands on the horizontal rock band above. Traverse left on hands to the offwidth and climb up the offwidth. Large pieces protect this well. We used a #7 Tricam and a #6 Camalot. Belay at the end of the offwidth off a single bolt or move up another 20 feet to a ledge and set up a more comfy belay. P3 - 5.9 on the left edge of the ledge is a sparse line of older bolts (not the nice new line of matolious bolts in the middle of the ledge.). The bolts aren't well placed as any fall will put you on a ledge. Climb this series of ledges with fun face climbing in between until the clean rock runs out and you are at the bottom of an aerate of broken rock. Scramble up the broken rock aerate. Be careful as there is lots of loose rock. Just before the top move left to the Northwest face of the dome and you will see a 2 bolt belay/repel by a tree. Descent - there are several choices. 1 Scramble to the top and around the Sheepshead gully (same as Mystery). Or 2 Make 2 double rope repels from the anchors at P3 to the ground then a short scramble back to the base of the climb. Or 3, my favorite choice, do the first double rope repel which lands you at the belay after the Wedge on Mystery then climb the last 3 pitches of Mystery. Either way, be sure to run up to the south side of the treed gully on top and do Scott's incredibly fun last Mystery pitch to the true summit of Muttonhead. Look for a bolt about 10 feet up.
Follow the same general approach for the Sheepshead. Once you reach the base of the Sheepshead take the trail that heads westward along the base of the formation and starts heading up the gully between the Sheepshead and the Muttonhead. After about five minutes there will be a faint climbers trail that diverges from the main trail and heads west. Take this trail for another five minutes and you will arrive at the Southwest face of the Muttonhead dome. On the far left of the face you will see a bolt line on the edge of a left facing dihedral. To the right of this bolt line you will see a broken system of cracks.