Siq al-Barid — "the cold canyon" — is a miniature version of Petra a few kilometres north, believed to have served as a suburb or caravan stop for Petra's Nabataean traders. It has its own carved facades, dining halls, and even faint traces of original painted ceilings, but almost none of the crowds. Most people see it in under an hour, which makes it an easy add-on rather than a full detour.
Little Petra is about 15 minutes north of Petra by road, making it an easy same-day add-on before or after the main site rather than a separate trip.
Same window as Petra — spring and autumn for comfortable temperatures, though Little Petra's narrower canyon offers more shade than Petra's open areas, so it's more forgiving in summer heat.
Go here either right before or right after Petra, not as a separate day — most guides build it into the same itinerary. If you're an experienced hiker, there's also a back-route trail connecting Little Petra to Petra itself, though it needs a guide and isn't something to attempt without one.