Purpose: Deformable registration of preoperative and intraoperative images facilitates accurate localization of target and critical anatomy in image-guided spine surgery. However, conventional deformable registration fails to preserve the morphology of rigid bone anatomy and can impart distortions that confound high-precision intervention. We propose a constrained registration method that preserves rigid morphology while allowing deformation of surrounding soft tissues. Method: The registration method aligns preoperative 3D CT to intraoperative cone-beam CT (CBCT) using free-form deformation (FFD) with penalties on rigid body motion imposed according to a simple intensity threshold. The penalties enforced 3 properties of a rigid transformation - namely, constraints on affinity (AC), orthogonality (OC), and properness (PC). The method also incorporated an injectivity constraint (IC) to preserve topology. Physical experiments (involving phantoms, an ovine spine, and a human cadaver) as well as digital simulations were performed to evaluate the sensitivity to registration parameters, preservation of rigid body morphology, and overall registration accuracy of constrained FFD in comparison to conventional unconstrained FFD (denoted uFFD) and Demons registration. Result: FFD with orthogonality and injectivity constraints (denoted FFD+OC+IC) demonstrated improved performance compared to uFFD and Demons. Affinity and properness constraints offered little or no additional improvement. The FFD+OC+IC method preserved rigid body morphology at near-ideal values of zero dilatation (D = 0.05, compared to 0.39 and 0.56 for uFFD and Demons, respectively) and shear (S = 0.08, compared to 0.36 and 0.44 for uFFD and Demons, respectively). Target registration error (TRE) was similarly improved for FFD+OC+IC (0.7 mm), compared to 1.4 and 1.8 mm for uFFD and Demons. Results were validated in human cadaver studies using CT and CBCT images, with FFD+OC+IC providing excellent preservation of rigid morphology and equivalent or improved TRE. Conclusions: A promising method for deformable registration in CBCT-guided spine surgery has been identified incorporating a constrained FFD to preserve bone morphology. The approach overcomes distortions intrinsic to unconstrained FFD and could better facilitate high-precision image-guided spine surgery.