  Using the Reduced Basis approach, we efficiently compress and accurately
represent the space of waveforms for non-precessing binary black hole
inspirals, which constitutes a four dimensional parameter space (two masses,
two spin magnitudes). Compared to the non-spinning case, we find that only a
{\it marginal} increase in the (already relatively small) number of reduced
basis elements is required to represent any non-precessing waveform to nearly
numerical round-off precision. Most parameters selected by the algorithm are
near the boundary of the parameter space, leaving the bulk of its volume
sparse. Our results suggest that the full eight dimensional space (two masses,
two spin magnitudes, four spin orientation angles on the unit sphere) may be
highly compressible and represented with very high accuracy by a remarkably
small number of waveforms, thus providing some hope that the number of
numerical relativity simulations of binary black hole coalescences needed to
represent the entire space of configurations is not intractable. Finally, we
find that the {\it distribution} of selected parameters is robust to different
choices of seed values starting the algorithm, a property which should be
useful for indicating parameters for numerical relativity simulations of binary
black holes. In particular, we find that the mass ratios $m_1/m_2$ of
non-spinning binaries selected by the algorithm are mostly in the interval
$[1,3]$ and that the median of the distribution follows a power-law behavior
$\sim (m_1/m_2)^{-5.25}$.
