Withdrawal of a point-in-time snap copy relationship or a portion of such a relationship, is managed in a manner which can obviate disruption of consistency groups due to the withdrawal. If the withdrawal request is directed to a subrange of the original snap copy relationship, the snap copy relationship is split by creating one or more point-in-time snap copy relationships over one or more subranges of tracks of the snap copy source. A determination is made as to whether to delay execution of the withdrawal request to temporarily preserve data of the withdrawal range. Disruptions to completion of consistency groups may be avoided by selectively delaying the withdrawal of a snap copy relationship corresponding to the withdrawal subrange. In so far as the host is involved, a host may treat the withdrawal request as immediately granted without delay. Other aspects may be realized, depending upon the particular application.