A system-initiated alter for an eligible cache structure with data elements may also begin in an attempt to avoid reclaims for directory entries. Structure full monitoring assumes directory entry reclaims are imminent when the total in use (changed and unchanged) percentage of directory entries exceeds 95% of the total directory entries. When this threshold has been exceeded a system-initiated alter may begin. In this case, the structure size is not expanded, but the structure objects may be reapportioned so as to provide more cache directory entries at the expense of data elements. System-initiated alter processing will only attempt to increase the entry/element ratio to a maximum value of 255:1.