A feasible approach to spectral color management was previously defined to include lookups performed within an interim connection space (ICS). The ICS is situated between a high-dimensional spectral profile connection space and output units. The definition of ICS axes and the minimum number of ICS dimensions are explored through consideration of LabPQR, an ICS described in earlier work. LabPQR has three colorimetric dimensions (CIELAB) and additional dimensions to describe a metameric black (PQR). Several versions of LabPQR are explored. One type defines PQR axes based on metameric blacks generated from Cohen and Kappauf's spectral decomposition. The second type is constructed in an unconstrained way where metameric blacks are statistically derived based on the spectral characteristics of the target output device. For a six-dimensional LabPQR, one that uses three colorimetric and three metameric black dimensions, it was found that Cohen and Kappauf-based LabPQR was inferior for estimating the spectra when compared to the unconstrained method. However, when the limited spectral gamut of an output device was introduced through printer simulation and necessary spectral gamut mapping, the disadvantage of six-dimensional Cohen and Kappauf-based LabPQR dissipated. On the other hand, reducing LabPQR to only five-dimensions (two metameric black dimensions) reintroduced the advanatage of the unconstrained approach even after virtual printer was consulted and spectral gamut mapping calculated. Importantly, it was found that the five-dimensional unconstrained approach achieved equivalent levels of performance to a full 31-dimensional approach within simulated printer spectral gamut limitations.