Three-body loss resonances associated with heavy-heavy-light Efimov states have been observed for over a decade in ultracold mixtures tuned near interspecies Feshbach resonances. For light-light-heavy systems, observing such resonances has been far more challenging due to the substantially large Efimov spacing. In these Efimov-unfavored systems, the intraspecies scattering length $a_{\text{BB}}$ has been shown to significantly affect the overall Efimov scenario, namely, the positions of the Efimov resonances $a_{-}^{\left(n\right)}$ and the three-body parameter (3BP) $a_{-}^{\left(0\right)}$. The present article explains the origin behind this influence by highlighting two primary mechanisms via which both the magnitude and sign of $a_{\text{BB}}$ govern the Efimov spectrum and set the resulting 3BP $a_{-}^{\left(0\right)}$. By employing van der Waals interactions for ${{}^{23}\mathrm{Na}}_2{}^{40}\mathrm{K}$, we attribute the vital role of $a_{\text{BB}}$ in Efimov-unfavored systems to the large difference between the Efimov scaling parameters for two and three resonant interactions, $s_0$ and $s_0^{*}$. In particular, we account for the unusually large $a_{-}^{\left(0\right)}$ obtained in light-light-heavy systems with $a_{\text{BB}}>0$ (e.g., ${{}^{41}\mathrm{K}}_2{}^{87}\mathrm{Rb}$), and show that the first Efimov resonance can still occur at an experimentally accessible value when $a_{\text{BB}}<0$.

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• Bose-Fermi mixtures
• Cold and ultracold molecules
• Efimov states
• Ultracold collisions