The resistivity of copper under hydrostatic pressures up to 3000 atm has been measured at temperatures between 4 degrees K and room temperature. Two specimens of commercially pure copper (99$\cdot $98%) and an alloy of 0$\cdot $056 at.% iron in copper were studied, the alloy being chosen because it showed a large resistance minimum. The effect of pressure on the ideal resistivity is in good agreement with Gruneisen's theory. There were some theoretical reasons for expecting that the alloy would have a large pressure coefficient of resistivity at or below the temperature of the resistance minimum. The pressure coefficient at these temperatures was, however, quite small and similar in value to the pressure coefficients of residual resistivity of the two purer specimens. Both the residual resistivity of the alloy and its pressure coefficient appeared to be strongly dependent on temperature.