High global and domestic demand for parrots (Psittaciformes) as pets, and consequent removal from the wild for the illicit trade have significantly contributed to their severe decline worldwide. While the trade is vast, not every parrot species is at equal risk of being traded, and there is controversy concerning the role of demand and the opportunity-based factors driving the illicit wildlife trade. The criminological model CRAAVED was used to analyze the factors associated with traded parrots in Indonesia, the country shown to have the highest priority for parrot conservation. We quantified the relative importance of CRAAVED components that drive trade risk by using advanced multivariate, phylogenetically controlled models. Three factors were significantly predictive of trade variation, whether the species was disposable (i.e. most legally exported species), enjoyable (i.e. most attractive), and accessible by people, suggesting that demand- and opportunity-based factors together can partially explain the illegal parrot trade in Indonesia. Our analysis has important implications for parrot conservation and the broader illegal pet trade, and is of considerable value for developing strategies at national and international levels for helping to control wildlife trade.