An iterative halftoning method with a space-variant, input-dependent control of the binarization noise is presented. The algorithm is based on experiences with the iterative Fourier transform algorithm. It uses a convolution with an appropriately chosen finite impulse response (FIR) filter and a spatial operation instead of the Fourier transform and spectral operation. An adaptation of the spectral properties to the local grayvalue of the input image is demonstrated. Besides the local grayvalue the local image gradient is considered. Incorporation of the information about the direction of the local gradient is possible by using a non-symmetric impulse response. The idea is to preserve the spatial frequency content of the image along the gradient at the expense of the content perpendicular to it. The control of the various free parameters of this halftoning method is discussed. Experiments with a gradient- adaptive, space-variant impulse response according to a local transfer function covering elliptic areas show an improved reproduction of high frequencies in the binary image.