Issues in the accuracy of preparing and using isoline maps of mean precipitation are reconsidered. A simulation is created to illustrate the concepts of discontinuous distribution and the effects of sampling on the resulting maps. The actual rainfall field is more closely represented as the number of rainfall events considered and the grid density increase. Data from Israel are used to provide concrete illustrations. A method of interpolating to a fine grid is proposed, using a regression model of station precipitation related to geographical variables of latitude, longitude, and elevation.