We describe a class of techniques whereby a laser frequency can be stabilized to a fixed optical cavity resonance with an adjustable offset, providing a wide tuning range for the central frequency. These techniques require only minor modifications to the standard Pound-Drever-Hall locking techniques and have the advantage of not altering the intrinsic stability of the frequency reference. In a laboratory investigation the sideband techniques were found to perform equally well as the standard, non-tunable Pound-Drever-Hall technique, each providing more than four decades of frequency noise suppression over the free-running noise. An application of a tunable system as a pre-stabilization stage in a phase-lock loop is also presented with the combined system achieving a frequency noise suppression of nearly twelve orders of magnitude.