We demonstrate a simple and versatile method to greatly extend the tuning range of optical frequency shifting devices, such as acousto-optic modulators (AOMs). We use this method to stabilize the frequency of a tunable narrow-band continuous-wave (CW) laser to a transmission maximum of an external Fabry-Perot interferometer (FPI) with a tunable frequency offset. This is achieved through a servo loop which contains an in-loop AOM for simple radiofrequency (RF) tuning of the optical frequency over the full 30 GHz mode-hop-free tuning range of the CW laser. By stabilizing the length of the FPI to a stabilized helium-neon (HeNe) laser (at 5 THz offset from the tunable laser) we simultaneously transfer the ∼ 1 MHz absolute frequency stability of the HeNe laser to the entire 30 GHz range of the tunable laser. Thus, our method allows simple, wide-range, fast and reproducible optical frequency tuning and absolute optical frequency measurements through RF electronics, which is here demonstrated by repeatedly recording a 27-GHz-wide molecular iodine spectrum at scan rates up to 500 MHz/s. General technical aspects that determine the performance of the method are discussed in detail. © 2013 Optical Society of America.