Human observers are very sensitive to a loss of image texture in photo-realistic images. For example a portrait image without the fine skin texture appears unnatural. Once the image is decomposed by a wavelet transformation, this texture is represented by many wavelet coefficients of low- and medium-amplitude. The conventional encoding of all these coefficients is very bitrate expensive. Instead, such an unstructured or stochastic texture can be modeled by a noise process and be characterized with very few parameters. Thus, a hybrid scheme can be designed that encodes the structural image information by a conventional wavelet codec and the stochastic texture in a model-based manner. Such a scheme, called WITCH (Wavelet-based Image/Texture Coding Hybrid), is proposed. It implements such an hybrid coding approach, while nevertheless preserving the features of progressive and lossless coding. Its low computational complexity and the parameter coding costs of only 0.01 bpp make it a valuable extension of conventional codecs. A comparison with the JPEG2000 image compression standard showed that the WITCH-scheme achieves the same subjective quality while increasing the compression ratio by more than a factor of two.