  We have carried out measurements of the pressure dependence to 1.2 GPa of the
oxygen isotope effect on $T_c$ in the high-$T_c$ superconductor
YBa$_2$Cu$_4$O$_8$ using a clamp cell in a SQUID magnetometer. This compound
lies close to, but just above, the 1/8$^{th}$ doping point where in
La$_{2-x}$Sr$_x$CuO$_4$ marked anomalies in isotope effects occur. Both
isotopes show the same very large pressure dependence of $T_c$ with the result
that the isotope exponent remains low ($\sim$0.08) but increases slightly with
increasing pressure. This is discussed in terms of stripe suppression, a
competing pseudogap and the effect of superconducting fluctuations.
