The value of seasonal energy storage depends on how the firm operates storage to capture seasonal price spreads. Energy storage operations typically face limited operational flexibility characterized by the speed of storing and releasing energy, which makes the optimal policy, in general, difficult to compute. A widely used practice-based heuristic, the rolling intrinsic (RI) policy, generally performs well compared with an optimal policy but can significantly underperform in some cases. In this paper, we aim to understand the gap between the RI policy and the optimal policy and leverage the resulting insights to improve the RI policy. A new heuristic policy, the price-adjusted rolling intrinsic (PARI) policy, is developed based on theoretical analysis of storage options. This heuristic adjusts certain prices before applying the RI policy to provide the RI policy with estimates of the values of various storage options. We evaluate the performance of the RI and PARI polices using actual data from the natural gas industry. Our results show that, on average, the PARI policy recovers about 67% of the value loss of the RI policy. Furthermore, when the value loss of the RI policy is larger, the PARI policy tends to recover a higher fraction of that value loss.