A versatile asymmetric synthesis of bicyclic pyrazolidinones through alkaloid-catalyzed formal [3 + 2]- and [3 + 2 + 2]-cycloadditions of ketenes with azomethine imines is described. The methodology was found to be tolerant of ketene and a variety of monosubstituted ketenes (R = alkyl, OAc). The products were formed in good to excellent yields (71-99% for 24 examples, 39 examples in all), with good to excellent diastereoselectivity in many cases (dr 3:1 to 27:1 for 22 examples), and with excellent enantioselectivity for most examples (≥93% ee for 34 products). In the case of most disubstituted ketenes, the reaction proceeded through a [3 + 2 + 2]-cycloaddition to form structurally interesting bicyclic pyrazolo-oxadiazepinediones with moderate diastereoselectivity (dr up to 3.7:1) and as racemic mixtures (3 examples). The method represents the first unambiguous example of an enantioselective reaction between ketenes and a 1,3-dipole.