  We report measurements of the pressure dependence of the superconducting
transition temperature T_c in single crystal samples of the rare-earth doped
superconductor Ca$_{0.73}$La$_{0.27}$Fe$_2$As$_2$. We track T_c with two
techniques, via in-plane resistivity measurements and with a resonant tunnel
diode oscillator circuit which is sensitive to the skin depth. We show that
initially T_c rises steeply with pressure, forming a superconducting dome with
a maximum T_c of ~44 K at 20 kbar. We discuss this observation in the context
of other electron-doped iron pnictide superconductors, and conclude that the
application of pressure offers an independent way to tune T_c in this system.
