Eukaryotic mRNA deadenylation is generally considered as a two-step process in which the PAN2–PAN3 complex initiates the poly(A) tail degradation while, in the second step, the CCR4-NOT complex completes deadenylation, leading to decapping and degradation of the mRNA body. However, the mechanism of the biphasic poly(A) tail deadenylation remains enigmatic in several points such as the timing of the switch between the two steps, the role of translation termination and the mRNAs population involved. Here, we have studied the deadenylation of endogenous mRNAs in human cells depleted in either PAN3 or translation termination factor eRF3. Among the mRNAs tested, we found that only the endogenous ATF4 mRNA meets the biphasic model for deadenylation and that eRF3 prevents the shortening of its poly(A) tail. For the other mRNAs, the poor effect of PAN3 depletion on their poly(A) tail shortening questions the mode of their deadenylation. It is possible that these mRNAs experience a single step deadenylation process. Alternatively, we propose that a very short initial deadenylation by PAN2-PAN3 is followed by a rapid transition to the second phase involving CCR4-NOT complex. These differences in the timing of the transition from one deadenylation step to the other could explain the difficulties encountered in the generalization of the biphasic deadenylation model.