Hyperfine structures have been investigated for odd-parity 4d25s5p and 4d35p levels for six 91Zr I transitions in the spectral range 458–549 nm using Doppler-free saturated absorption spectroscopy in a sputtered vapour. The measured hyperfine structure constants, A and B, together with results of previous studies were analysed by means of a parametric method. The interpretation was based on refined multiconfigurational fine structure calculations, which include the main Rydberg series configuration states. The analysis suggests a drastic revision of the composition of the 4d5s25p configuration levels. The main one-electron hyperfine structure parameters for the lowest configuration, i.e. 4d25s5p, are determined to be a10 5s = −2672(61) MHz, a01 4d = −115.8(3.4) MHz, a01 5p = −127.4(3.7) MHz, b02 4d = −93.5(2.8) MHz and b02 5p = −139.9(5.1) MHz. These values are in excellent agreement with ab initio calculations, justifying our choice of the perturbing configuration states.