The crystal structure of the enzyme Dicer from Giardia intestinalis was solved to 3.3 A resolution by MAD using crystals belonging to space group P2(1)2(1)2 [Macrae et al. (2006), Science, 311, 195-198]. These crystals were derived from crystals that diffracted X-rays to 3.0 A resolution but were refractory to structure determination because they were twinned. It is shown here that the original Dicer crystals represent an unusual case of perfect pseudo-merohedral twinning of orthorhombic crystals. Before the twinning problem was overcome, it was possible to calculate a low-resolution electron-density map in space group P4(1) that was used to build a partial molecular model. Experimental phases were sufficient to identify heavy-atom sites that indicated space-group inconsistency, leading to identification of the true space group. This information guided the search for different crystallization conditions that yielded untwinned crystals and ultimately a fully interpretable electron-density map.