Coded aperture snapshot spectral imaging (CASSI) provides a mechanism for capturing a 3D spectral cube with a single shot 2D measurement. In many applications selective spectral imaging is sought since relevant information often lies within a subset of spectral bands. Capturing and reconstructing all the spectral bands in the observed image cube, to then throw away a large portion of this data, is inefficient. To this end, this paper extends the concept of CASSI to a system admitting multiple shot measurements, which leads not only to higher quality of reconstruction but also to spectrally selective imaging when the sequence of code aperture patterns is optimized. The aperture code optimization problem is shown to be analogous to the optimization of a constrained multichannel filter bank. The optimal code apertures allow the decomposition of the CASSI measurement into several subsets, each having information from only a few selected spectral bands. The rich theory of compressive sensing is used to effectively reconstruct the spectral bands of interest from the measurements. A number of simulations are developed to illustrate the spectral imaging characteristics attained by optimal aperture codes.