Although you should definitely follow the Siq into Petra at least once (and probably more than once, at different times of day), if you’ve allocated several days to a visit, the beautiful Wadi Muthlim is a good alternative entry route through stunning scenery, but taking no less than two hours to deliver you to the Nymphaeum in the city centre. Due to the very real danger of flash floods, you shouldn’t attempt it at all during the rainy season – roughly November to March – and even as late as May, there may be difficult-to-avoid standing pools of water harbouring water snakes: wading would be a mistake.
Before beginning the walk, you can take a small detour from the dam at the Siq entrance up to the Eagle Niche, set in the rocks 400m to the northwest. Cross the wadi over the roof of the tunnel and head left up the second side-valley; it’s a short scramble over the smooth, hot rock up to a set of small niches carved in the right-hand wall, one of which features a strikingly carved eagle with wings outspread.
Back at the tunnel, Wadi Muthlim – full of oleanders, but with high walls cutting out all sound bar the occasional birdsong – is easily passable up to the remains of another Nabatean dam; beyond here, the path gets steadily narrower until you reach a point where a massive boulder all but blocks the way. It’s possible to squeeze past, and the path continues to narrow until, with the wadi floor no wider than your foot, you reach a T-junction; arrows on the solid walls all around will point you left. This cross-wadi is the Sidd Maajn, equally narrow, but beautifully eroded by flowing water. As you proceed, seemingly moving through the heart of the mountain, you’ll notice the Nabateans were here before you: there are dozens of carved niches, some featuring pediments, other curving horns. It’s around here that the way might be blocked by rockpools.
Eventually, you’ll emerge into the open Wadi Mataha, about 600m northeast of Dorotheos’ House, and the best part of 2km northeast of the Nymphaeum.