We present heat capacity, c-axis thermal expansion and pressure-dependent, low-field, temperature-dependent magnetization for pressures up to ∼12 kbar, data for KFe2As2 single crystals. Tc decreases under pressure with dTc/dP≈−0.10 K/kbar. The inferred uniaxial, c-axis, pressure derivative is positive, dTc/dpc≈0.11 K/kbar. The data are analyzed in comparison with those for overdoped Fe-based superconductors. Arguments are presented that superconductivity in KFe2As2 may be different from the other overdoped, Fe-based materials in the 122 family.