A mature oil field rescaled contraction describes a switch to a technological alternative more appropriate for the depleted state of an underlying resource. Off-shore oil rigs are an illustration, since the original technological scale designed for very large output flows becomes inappropriate as the operational efficiency declines later in life and facing a dwindling output flow, so a more appropriate extraction technology becomes economic. A real option representation is formulated on a stochastic oil price and deteriorating output volume. We consider investment/divestment decisions both separately, and jointly, which have different implications for government policies and also option values. The resulting model yields analytical (or semi-analytical) results indicating that immediate switching to the lower cost technology could sometimes be hastened as the price volatility increases, depending on the current revenue, if divestment and switching are considered jointly. However, greater volatility could also promote hysteresis.