We present a phenomenological analysis of the cosɸ and cos 2ɸ asymmetries in unpolarized semiinclusive deep inelastic scattering, based on the recent multidimensional data released by the COMPASS and HERMES collaborations. In the transverse-momentum-dependent framework, valid at relatively low transverse momenta, these asymmetries arise from intrinsic transverse momentum and transverse spin effects, and from their correlations. The role of the Cahn and Boer-Mulders effects in both azimuthal moments is explored up to order 1/Q. As the kinematics of the present experiments is dominated by the low-Q² region, higher-twist contributions tum out to be important, affecting the results of our fits. [ABSTRACT FROM AUTHOR]