We present a laser cooling scheme for trapped ions and atoms using a combination of laser couplings and a magnetic gradient field. In a Schrieffer-Wolff transformed picture, this setup cancels the carrier and blue sideband terms completely (up to first order in the Lamb-Dicke parameter), resulting in an improved cooling behaviour compared to standard cooling schemes in the Lamb-Dicke regime (e.g. sideband cooling) and allowing cooling to the vibrational ground state. A condition for optimal cooling rates is presented and the cooling behaviour for different Lamb-Dicke parameters and spontaneous decay rates is discussed. Cooling rates of one order of magnitude less than the trapping frequency are achieved using the new cooling method. Furthermore, the scheme exhibits fast rates and low final populations, even for significant deviations from the optimal parameters, and provides good cooling rates also in the multi-particle case.