The phrase "tasselled out" typically refers to a decorative item or piece of clothing that is adorned with tassels, such as a purse or scarf. Some synonyms for this term might include "festooned," "embellished," "ornamented," or "adorned." Additionally, the word "fringed" could be used to describe an item that has a similar decorative border made up of small fibers or strands. Depending on the context, other synonyms for "tasselled out" might include "decorated," "beaded," "bejeweled," or "bedecked." Ultimately, the best synonym for this term will depend on the specific situation and the writer's intended meaning.