Recent experimental developments of high‐resolution NMR in solids (for example, double rotation and dynamic‐angle spinning) address the reduction of second‐order line broadening effects, particularly in systems involving quadrupolar nuclei such as ²³Na, ¹⁷O, ²⁷Al, and ¹⁴N. However, some aspects of the theoretical description of these systems have not been clearly understood; in particular, the various procedures available to truncate the interactions give incompatible results. We present a general framework, based on static perturbative methods, which provides a natural procedure to derive the correct Hamiltonian for higher‐order effects in irreducible tensor form. Applications of this method to coherent averaging techniques (sample motion or radio‐frequency irradiation) are described and compared to previous treatments based on average Hamiltonian theory.