Intentional manipulation of invoices that lead to undervaluation of trade goods is the most common type of customs fraud to avoid ad valorem duties and taxes. To secure government revenue without interrupting legitimate trade flows, customs administrations around the world strive to develop ways to detect illicit trades. This paper proposes DATE, a model of Dual-task Attentive Tree-aware Embedding, to classify and rank illegal trade flows that contribute the most to the overall customs revenue when caught. The strength of DATE comes from combining a tree-based model for interpretability and transaction-level embeddings with dual attention mechanisms. To accurately identify illicit transactions and predict tax revenue, DATE learns simultaneously from illicitness and surtax of each transaction. With a five-year amount of customs import data with a test illicit ratio of 2.24%, DATE shows a remarkable precision of 92.7% on illegal cases and a recall of 49.3% on revenue after inspecting only 1% of all trade flows. We also discuss issues on deploying DATE in Nigeria Customs Service, in collaboration with the World Customs Organization.