This pilot study set out to assess the speaker discriminatory power asymmetry regarding parameters from different phonetic dimensions in spontaneous speech, i.e., spectral, melodic, and temporal. The speech material consisted of spontaneous telephone conversations between siblings. The participants were 20 male subjects, Brazilian Portuguese speakers from the same dialectal area. Six acoustic-phonetic parameters were chosen for the comparison: f0 median, f0 baseline, speech rate, articulation rate, F3, and F4. Overall, acoustic parameters pertaining to the speech tempo category depicted the worse performance in terms of speaker discriminatory power when assessed in isolation. Such a trend was indicated by the relatively higher median and mean Cllr and EER values. Moreover, from the set of parameters assessed, high formant frequencies, i.e., F3 and F4, were the bestperforming estimates in terms of discriminability depicting the lowest EER and Cllr values. The results suggested a speaker discriminatory power asymmetry concerning different acoustic-phonetic parameters, in which speech tempo estimates presented a lower discriminatory power when compared to melodic and spectral parameters. The findings also suggest that data sampling is crucial for the reliability of Cllr and EER calculations.