Scanning tunneling microscopes (STMs) are usually operated in current-feedback mode when scanning over wide areas or rough surfaces. The speed of image acquisition is determined by the scanning rate, which (in this mode) is limited by the bandwidth of the feedback control loop. The control loop bandwidth is usually restricted to frequencies lower than the lowest mechanical resonant frequency (f(r)) of the STM scanner and tip. This resonant frequency is typically in the range 5-15 kHz and is generally ascribed to mechanical resonance of the piezoelectric scanner tube or scanner tripod. In this article we describe some measured sources of mechanical resonance in STMs, and present a design which eliminates the need to control the scanner at high frequencies. We have established that the lowest mechanical resonance mode may be ascribed to the base mounting structure (in addition to the scanning actuator), depending on the specific design. The complex origins of this mode prevent the use of conventional control techniques at frequencies above f(r). We have developed an STM design in which a separate feedback actuator is used to modulate the z position of the sample, independently to the scanning (x and y) actuator. The effective resonance frequency of this actuator is extremely high (in excess of 100 kHz) and the control bandwidth is correspondingly improved.