Embeddings extracted by deep neural networks have become the state-of-the-art utterance representation in speaker recognition systems. It has recently been shown that incorporating frame-level phonetic information in the embedding extractor can improve the speaker recognition performance. On the other hand, in the final embedding, phonetic information is just an additional source of session variability which may be harmful to the text-independent speaker recognition task. This suggests that at the embedding level phonetic information should be suppressed rather than encouraged. To verify this hypothesis, we perform several experiments that encourage or/and suppress phonetic information at various stages in the network. Our experiments confirm that multitask learning is beneficial if it is applied at the frame-level stage of the network, whereas adversarial training is beneficial if it is used at the segment-level stage of the network. Additionally, the combination of these two approaches improves the performance further, resulting in an equal error rate of 3.17% on the VoxCeleb dataset.