The structures and rotational constants of prototypical monocyclic terpenes and terpenoids have been analyzed by a general computational strategy based on recent Pisa composite schemes (PCS) and vibrational perturbation theory at second order (VPT2). Concerning equilibrium geometries, a one-parameter empirical correction is added to bond lengths obtained by the revDSD-PBEP86 double hybrid functional in conjunction with a slightly modified cc-pVTZ-F12 basis set. The same functional and basis set give accurate harmonic frequencies, whereas the cheaper B3LYP hybrid functional in conjunction with a double-ζ basis set is employed to compute the semidiagonal cubic force constants needed to obtain vibrational corrections to the rotational constants in the framework of the VPT2 model. The final results obtained in this way show in most cases average deviations with respect to the experiment close to 0.1%, which correspond to errors around 1 mÅ and 0.1° for bond lengths and valence angles, respectively. The accuracy of the results has produced reliable estimates for species not analyzed yet experimentally. In addition to the intrinsic interest of the studied molecules, this article confirms that high-resolution spectroscopic studies of quite large systems can now be aided by a very accurate yet robust and user-friendly computational tool.