Peredo et al. (1995) derived a frequently used three-dimensional bow shock model parameterized by the upstream Alfv¿nic Mach number from the set of approximately 550 bow shock crossings provided by 17 distinct spacecraft over the period of 1963--1980. However, several studies reported some systematic biases in the bow shock model predictions. Therefore we have attempted to improve upon the bow shock model of Peredo et al. (1995) using their original data set and methodology in an effort to better understand these effects. We have performed three-dimensional best fits to the bow shock crossings binned by the upstream Mach numbers MA, MS, and MMS and found that the best fitting surfaces were best ordered with the MA. In agreement with predictions from the magnetohydrodynamic theory, the results show that the bow shock surface expands when the MA decreases. The found dawn-dusk asymmetry in the bow wave is consistent with previous studies only in the Geocentric Plasma Ecliptic System (GPE) coordinates but not in the Geocentric Interplanetary Medium (GIPM) coordinates which suggests that the employed data set is not comprehensive enough for resolving this asymmetry. Nor is the Mach cone asymmetry resolved in our data set (not even in the GIPM frame). We have derived two models predicting the statistical position and shape of the bow shock in the GPE or GIPM coordinates. Error analysis shows that the GPE-based model is more accurate and applicable for MA = 3--20 except the nose region where the model underestimates the bow shock position for MA < 5. A direct comparison of the model predictions with 5870 IMP 8 bow shock crossings demonstrated high accuracy of predictions and, for the GPE-based model, an exceptional stability of predictions even under extreme upstream conditions. Indeed, the new GPE-based bow shock model is more accurate and equally or more stable than the Formisano (1979), Nemecek and Šafr¿nkov¿ (1991), Farris and Russell (1994), Cairns and Lyon (1995), Peredo et al. (1995), or Verigin et al. (2001) models.