New pressure and pressure-derivative functions for analyzing well-test data are presented. The new pressure function represents the integral of pressure with respect to time divided by time. Thus, this new pressure function represents a moving or cumulative average of the pressure over time. It is shown that the logarithmic derivative of this pressure function is equal to a moving or cumulative average of the standard logarithmic pressure derivative. It also is shown that this new derivative function is useful for analyzing well-test pressure data in cases where the pointwise pressure-derivative data are difficult to interpret because of noise.