Ex-post split-award auctions are a frequently used form of combinatorial auction mechanism in practice. The procurement quantity is split into several shares and suppliers can submit bids on separate shares as well as on the entire quantity. Markets with diseconomies of scale are wide-spread, but strategically challenging. In a game-theoretical equilibrium analysis, Kokott et al. (2019) have recently shown that in contrast to single-object auctions, there is no strategic equivalence between first-price sealed-bid (FPSB) and Dutch combinatorial auctions. The FPSB auctions are characterized by efficient and inefficient equilibria while the Dutch auctions only possess efficient equilibria. We report the results of extensive laboratory experiments and show that the theory explains the bid data surprisingly well. Importantly, a compound Dutch auction format weakly outperforms the wide-spread combinatorial first-price sealed-bid auction in efficiency and total procurement costs. The results provide guidance for procurement managers in the field.