The improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO-CASCI) method is a simplified CAS self-consistent field (SCF), CASSCF, method. Unlike the CASSCF approach, the IVO-CASCI method does not require iteration; beyond an initial SCF calculation, rendering the IVO-CASCI scheme computationally more tractable than the CASSCF method and devoid of the convergence problems that sometimes plague CASSCF calculations. as the CAS size increases, while retaining all the essential positive benefits of the CASSCF method. Earlier applications demonstrate that the IVO-CASCI energies are at least as accurate as those from the CASSCF and provide the impetus for our recent development of the analytical derivative procedures that are necessary for a wide applicability of the IVO-CASCI approach. Here we test the ability of the analytic energy gradient IVO-CASCI approach (which can treat both closed- and open-shell molecules, of arbitrary spin multiplicity) to compute the equilibrium geometries of four organic radicaloid species, namely, (i) the diradicals trimethylenemethane (TMM), 2,6-pyridyne, and the 2,6-pyridynium cation and (ii) a triradical 1,2,3-tridehydrobenzene (TDB), using various basis sets and different Choices for the active space. Although these systems and relaxed molecules have fascinated theoretical chemists for many years, their strong multireference character makes their description quite difficult with most standard many-body approaches. Thus, they provide ideal tests to assess the performance of the IVO-CASCI method. The present work demonstrates consistent agreement with far more expensive benchmark state-of-the-art ab calculations and thereby indicates that this new gradient method is able to describe the geometries of various radicaloids very accurately, even when small, but qualitatively correct, reference spaces are used. For example, the IVO-CASCI method leads to a monocyclic structure for the 2,6-isomers of the didehydropyridinium (pyridynium) cation and of didehydropyridine (pyridyne), while SCF and single-reference CCSD computations predict an incorrect bicyclic structure. The IVO-CASCI structures and relative stability for the ground (2)A(1) and excited B-2(2) states of TDB also accord with the experimentally observed IR spectra and with other highly sophisticated theoretical calculations. The blend of accuracy and reduction in computational cost offered by the present IVO-CASCI analytical gradient method clearly demonstrates that the method provides a practical avenue for studying the geometries of various radicaloid species of different levels of complexity.