Recently, it has been argued that various measures of supersymmetric naturalness—electroweak, Higgs mass and EENZ/BG—when applied consistently, concur with one another and make very specific predictions for natural supersymmetric spectra. Highly natural spectra are characterized by light Higgsinos with mass not too far from $m_h$ and well-mixed but TeV-scale third generation squarks. We apply the unified naturalness measure to the case of heavy Higgs bosons $A$, $H$ and $H^{\pm }$. We find that their masses are bounded from above by naturalness depending on $\tan \beta$: e.g. for 10% fine-tuning and $\tan \beta \sim 10$, we expect $m_A\lesssim 2.5\mathrm{TeV}$ whilst for 3% fine-tuning and $\tan \beta$ as high as 50, then $m_A\lesssim 8\mathrm{TeV}$. Furthermore, the presence of light Higgsinos seriously alters the heavy Higgs boson branching ratios, thus diminishing prospects for usual searches into standard model final states, while new discovery possibilities arise due to the supersymmetric decay modes. The heavy supersymmetric decay modes tend to be $H,A,H^{\pm }\to W,Z$, or $h+{\cancel{E}}_T+\text{soft tracks}$ so that single heavy Higgs production is characterized by the presence of high $p_T$ $W$, $Z$ or $h$ bosons plus missing $E_T$. These new heavy Higgs boson signatures seem to be challenging to extract from SM backgrounds.