The effects of pressure up to $sim 20$ kbar, on the structural phase transition of SrFe$_2$As$_2$ and lightly Sn-doped BaFe$_2$As$_2$, as well as on the superconducting transition temperature and upper critical field of (Ba$_{0.55}$K$_{0.45}$)Fe$_2$As$_2$ single crystals have been studied. All the transition temperatures decrease with pressure in an almost linear fashion. Under pressure, the upper critical field curve, $H_{c2}(T)$, for (Ba$_{0.55}$K$_{0.45}$)Fe$_2$As$_2$ shifts down in temperature to follow the zero field $T_c$ with very little change in slope. Composite $P - T$ phase diagrams for three parent compounds, AFe$_2$As$_2$ (A = Ba, Sr, Ca), are constructed and appear to be remarkably similar: (i) having a structural (antiferromagnetic) phase transition line with a negative slope and (ii) showing signs of the emerging superconducting state at intermediate pressures.
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