Until MacKenzie recently emphasized the dominating role of space charge beam blowup at small radii in synchrocyclotrons, the importance of this factor was not appreciated. Much largely futile effort had been expended on attempts to increase average beam currents by improving other factors. Lawson's extension of MacKenzie's treatment for ordinary cyclotrons is considered in more detail, with numerical examples and a detailed discussion of the extension of the theory to synchrocyclotrons. In addition, a simpler semi‐empirical formula is obtained which gives a good match to existing currents in all present synchrocyclotrons. Current gains up to a factor ∼100 should be feasible, and a discussion is given as to how such an improvement might be gained by modifications of existing synchrocyclotrons.