When your overall hand strength is tightly defined then you are obligated to cuebid if asked. Example: 1♠-(2♦)-3♦-(p)-3♠-(p)-4♣ There are some auctions that ask for a specific holding in some suit. For instance, if responder had bid 5♠ instead of 5♣ in the auction you posted, opener would be obligated to bid on with a diamond control no matter how much he had overbid his hand so far. If neither of the above apply, then I would say that you are not obligated to cuebid if you have a minimum.