Efficient, simple, and lossless methods for encoding and transmitting grey-scale and binary (B/W) pictures are described. The methods are such that an initial segment of the transmission permits the receiving device to construct an approximate picture; as transmission proceeds, the receiver progressively constructs better approximations. Some of the low-bandwidth channel usages include telebrowsing -where one wants to abort transmission of unwanted pictures as soon as they are recognized, and teleconferencing-where one wants to receive a gestalt first, followed by the details. In the method for grey-scale pictures, the transmitter first defines a hierarchical structure of picture subdivisions, and assigns, simply by table lookup, approximate average light values to all pairs of cells from the smallest size to that encompassing the entire picture. During tranmission the latter "primary" value is sent, followed by numbers which permit successive cell splitting, thus producing progressively finer picture representations in approximate values, culminating in an exact reconstruction at the pel level. A picture of p pels quantized into b bits each is perfectly reconstructed upon receipt of exactly b × p bits. If the recipient deems an intermediate version satisfactory, then "picture compression" is effectively achieved. This scheme thus provides some of the benefits of transform encoding (Fourier, Hadamard, Hotelling, singular-value decomposition) but with no truncation error and no need for handling coefficients of various sizes. Furthermore, computation varies only linearly with number of pels. The method for binary (B/W) pictures also involves a hierarchical structuring of the picture but with attention paid to picture compression-by declaring subdivisions, at as high a level as possible, to be solid black or solid white (and in need of no further description). Compressions thus achieved are 8:1 in cases where the "blob" coding method of Frank gives 11½:1