For special applications in spectroscopy, tunable single-frequency lasers are required to excite selectively relevant molecules. Amplified Yb:YAG disk lasers provide one opportunity for such lasers with a number of advantageous properties. Nevertheless, changing the wavelength from shot to shot at kHz repetition rates - desired e.g. for background subtraction or two-wavelength methods - remains challenging. We present results from two approaches, which in combination allow for fast wavelength switching of the oscillator and for extension of the tunability range of the laser system. For wavelength switching high voltage (some kV) is applied to a special birefringent filter (Lyot filter). Polarization rotation induced by the electric field yields losses at the wavelength emitted without voltage: the laser emits at a "new" wavelength with the highest gain. This new wavelength is determined by multiples of the free spectral range of the intra-cavity etalon used for single-frequency operation. The second stage of the laser system comprises an Yb:YAG regenerative amplifier. To ensure that parasitic lasing of this laser at the gain maximum is suppressed effectively, an additional birefringent filter is inserted into the amplifier. Adjusting this filter suppresses parasitic lasing and extends the tunability range of the system by a factor of more than 4.