We describe a general method of calculating exciton energies in shallow quantum wells. This technique is applicable to both single- and multiple-quantum-well systems, and is valid for both type-I and type-II systems, even under circumstances where the valence- and/or conduction-band offsets may be small compared to the exciton binding energy. Quantitative predictions of excitonic energies and relative intensities are made and compared with experimental data on a number of different shallow-well diluted magnetic semiconductor quantum well and superlattice systems. Based on these comparisons, it is shown that the model indeed provides a detailed description and analysis of the type-I type-II transition and the behavior of excitons in a spin superlattice. In addition, the model also predicts and describes certain additional phenomena, such as metastable above-gap excitons which should exist in certain type-II systems. Also, reentrant type-I type-II type-I transitions are predicted under some circumstances.