A method is described for processing fruit or vegetables, e.g., cranberries, into two different juices. One of the two juices has a relatively high level of acids. The other of the two juices has a relatively low level of acids. The method of the invention entails providing three juice streams. The first juice stream is passed through a nanofiltration apparatus or some other apparatus that is capable of preferentially removing acidic compounds from the raw fruit or vegetable juice feedstock. This process creates two juice fractions: a juice fraction that is relatively enriched in acids and a juice fraction that is relatively reduced in acids. The second juice stream is combined with the juice fraction that is relatively enriched in acids to create a juice that has a relatively high level of acids. The third juice stream is combined with the juice fraction that is relatively reduced in acids to create a juice that has a relatively low level of acids.