Compressive sensing (CS) is a new signal acquisition paradigm which shows that far fewer samples are required to reconstruct sparse signals than previously thought. Although most of the literature focuses on signals sparse in a fixed orthonormal basis, recently the Signal Space CoSaMP (SSCoSaMP) greedy method was developed for the reconstruction of signals compressible in arbitrary redundant dictionaries. The algorithm itself needs access to approximate sparse projection schemes, which have been difficult to obtain and analyze. This paper investigates the use of several different projection schemes and catalogs for what types of signals each scheme can successfully be utilized. In addition, we present novel hybrid projection methods which outperform all other schemes on a wide variety of signal classes.