Convergent intron loss in the plastid genome has been reported at a broad phylogenetic level in the flowering plants, but very few cases are known among closely related taxa, aside from those with a propensity for genome rearrangement. We performed a large survey of an intron in the plastid 3′-rps12 locus and found that it is present in all monocots sampled, apart from two closely related families in the order Asparagales, Asphodelaceae and Hemerocallidaceae. However, only a subset of taxa in the latter family lack it. A likelihood-based parametric bootstrapping analysis rejects an hypothesis that intron loss is a marker for the monophyly of all Asparagales lacking it. Reconstructions of evolutionary transformation in intron status (presence versus absence) using an equal weighting scheme (standard parsimony) on optimal and plausible suboptimal trees instead yield two major classes of ancestral-state assignment. These scenarios indicate that introns were either lost in parallel, or there was a single loss and a subsequent secondary origin. Parsimony weighting schemes that are skewed but (arguably) more realistic than equal weighting reject the latter reconstruction, and support the hypothesis that intron loss is not homologous in Asphodelaceae and Hemerocallidaceae. One of the parallel losses supports a recent circumscription of Hemerocallidaceae to incorporate the family Johnsoniaceae.