Provided are a computer program product, system, method, and data structure for compressing an input data stream. A determination is made of consecutive data units in the input data stream that match consecutive data units in a history buffer. A copy pointer symbol indicates a copy pointer symbol referencing previously received data units in the history buffer. A determination is made of a relative displacement count in the history buffer at which the number of matching consecutive data units start. A determination is made of a range of relative displacement counts comprising one of a plurality of ranges of displacement counts including the determined relative displacement count. A determination is made of the encoding scheme associated with the determined range. An encoding of the relative displacement count is determined from the determined encoding scheme. The determined encoding of the relative displacement count is indicated in the copy pointer.