Small boron clusters have been shown to be planar from a series of combined photoelectron spectroscopy and theoretical studies. However, a number of boron clusters are quasiplanar, such as B-7(-) and B-12(-). To elucidate the nature of the nonplanarity in these clusters, we have investigated the electronic structure and chemical bonding of two isoelectronic Al-doped boron clusters, AlB6- and AlB11-. Vibrationally resolved photo- electron spectra were obtained for AlB6-, resulting in an accurate electron affinity (EA) for AlB6 of 2.49 +/- 0.03 eV. The photoelectron spectra of AlB11- revealed the presence of two isomers with EAs of 2.16 +/- 0.03 and 2.33 +/- 0.03 eV, respectively. Global minimum structures of both AlB6- and AlB11- were established from unbiased searches and comparison with the experimental data. The global minimum of AlB6 is nearly planar with a central B atom and an A1B5 six membered ring, in contrast to that of B-7(-), which possesses a C-2 nu structure with a large distortion from planarity. Two nearly degenerate structures were found for AlB11- competing for the global minimum, in agreement with the experimental observation. One of these isomers with the lower EA can be viewed as substituting a peripheral B atom by Al in B-12(-), which has a bowl shape with a B-9 outer ring and an out-of-plane inner B-3 triangle. The second isomer of AlB11- can be viewed as an Al atom interacting with a B-11(-) cluster. Both isomers of AlB11- are perfectly planar. It is shown that Al substitution of a peripheral B atom in B-7(-) and B-12(-) induces planarization by slightly expanding the outer ring due to the larger size of Al.