Error diffusion, ordered dither, and patterning are well-known digital halftoning techniques, each with its advantages and disadvantages. Error diffusion is known for correlated artifacts looking like zebra stripes. Images produced by ordered dither and patterning suffer from artificial contours in slowly varying regions of pictures. Use of ordered matrices by both ordered dither and patterning results in poor rendition of small details, so the images appear blurred. We discuss how the modified Floyd-Steinberg error diffusion algorithm reduces correlated artifacts compared to the classical Floyd-Steinberg algorithm without increase in the amount of work. It also simplifies combining of error diffusion with other methods. We introduce two families of hybrid algorithms. One of them combines the modified Floyd-Steinberg algorithm with ordered dither and the other one combines it with patterning. We fight the correlated artifacts with ordered matrices while reducing the accompanying artificial contours by error diffusion. The latter achievement allows us to use smaller matrices and thus affect small detail representation at low resolutions. We show that hybrid algorithms are useful for digital simulation of classical screens. Combining error diffusion and patterning results in speedups essential for printing medical images at high resolutions. The article considers application of the hybrid algorithms to printing of medical images on laser printers.