Smart contracts can be used for the fair exchange of digital goods. A smart contract can escrow the exchange where the receiver deposits the payment, and the sender claims it by providing the goods. In the case of misbehavior, the parties provide proof on whether the received goods match the pre-agreed description or not. In general, the description is assumed to be the hash of the goods, and it is publicly known. However, without trusting the description provided by the sender, this assumption is not plausible for the scenarios where the goods are uniquely created for a specific receiver. To overcome the trust issue, sampling-based exchange protocols have been introduced where the parties use a sample of the goods as the description. Yet, the existing sampling-based proposals suffer from high on- and off-chain computational and storage costs. In this paper, we present FairDEx: an efficient sampling- based protocol that is suitable for the exchange of unique goods. Our description protocol allows us to achieve low on- and off-chain costs, which are independent of the size of the goods. The off-chain part of the protocol only utilizes highly efficient algorithms, namely hashing and symmetric key encryption. To illustrate the feasibility of FairDEx, we evaluate a research prototype on the Ethereum test network. Our results show that the cost of running FairDEx is around 0.6M gas for reasonably large sample sets, which is 30% cheaper than the state-of-the-art Ethereum-based proposals.@en