Using an ultrafast pump pulse affects the spectral and temporal characteristics of high order harmonics in an unexpected and fortuitous way. Calculations of spectra for rare gases using 10100fs, 800nm pulses show that as the pump pulse length decreases the highest harmonics become correspondingly shorter while their conversion efficiencies increase dramatically. Especially significant is that we find these highest harmonics have phase characteristics that allow for the possibility of compression to subfemtosecond time scales. {copyright} {ital 1997} {ital The American Physical Society}