The Small Wild Goose Pagoda was built in 707, so that's a few years after the Giant Wild Goose Pagoda. Although it is smaller than the other one, it has more "floors" (some are only one meter tall).
Originally, the tower was 45 meters tall, but an earthquake in 1487 destroyed the top two and opened a crack that went all the way from the top to the bottom. There was a gap of 30cm in the wall. But then, in 1521 another quake struck and "magically" put the building back together.
The mystery was revealed during restoration after 1949. The reason why the Small Wild Goose Pagoda can withstand dozens of earthquakes is that wise ancient craftsmen have formed its foundation as a hemisphere of rammed earth. In this way, pressure can be distributed evenly when an earthquake happens. Just like a never-fall doll, the flexible and stable pagoda can survive these storms and earthquakes. - Travel China Guide
The Xi'an Museum
Inside the same park as the Small Goose Pagoda is the Xi'an Museum. While you need to pay a ticket to access the pagoda, entry for the museum is free as long as you take your passport. It is smaller than the Shaanxi History Museum, but a lot less busy too, making the experience far more enjoyable.
I specially liked some of the statues there.