This paper describes novel methods for evoking a multichannel audio experience over stereo headphones. In contrast to the conventional convolution-based approach where, for example, five input channels are filtered using ten head-related transfer functions, the current approach is based on a parametric representation of the multichannel signal, along with either a parametric representation of the head-related transfer functions or a reduced set of head-related transfer functions. An audio scene with multiple virtual sound sources is represented by a mono or a stereo downmix signal of all sound source signals, accompanied by certain statistical (spatial) properties. These statistical properties of the sound sources are either combined with statistical properties of head-related transfer functions to estimate “binaural parameters” that represent the perceptually relevant aspects of the auditory scene or used to create a limited set of combined head-related transfer functions that can be applied directly on the downmix signal. Subsequently, a binaural rendering stage reinstates the statistical properties of the sound sources by applying the estimated binaural parameters or the reduced set of combined head-related transfer functions directly on the downmix. If combined with parametric multichannel audio coders such as MPEG Surround, the proposed methods are advantageous over conventional methods in terms of perceived quality and computational complexity.