Solar Tower with Thermal Energy Storage (ST-TES) represents a promising technology for large-scale exploitation of solar irradiation for electricity generation. A ST-TES plant has the potential to extend electricity generation to more favorable conditions, such as high electricity prices. The size of TES, however, constrains the flexibility of dispatching choices, especially when there is significant uncertainty in forecasts of solar irradiation and electricity prices. This study explores the impact of TES size when a ST-TES plant uses Model-Predictive Control (MPC) for dispatch planning. The performance of MPC is benchmarked against perfect knowledge (PK) and two day-ahead strategies. The optimal achievable profit for each TES size is determined using the PK strategy. An analysis is conducted to evaluate the relative profit losses for all the other simulated strategies compared to the PK strategy. A case study is conducted for a hypothetical 115 MWe STTES plant in South Australia. For January and August, 100 tests are performed for each dispatch policy, with the TES size varying from 6 to 14 hours. The revenue evaluation is conducted with both fixed and wholesale spot prices. The analysis shows that MPC-aided dispatching enables the adoption of a smaller TES compared to day-ahead policies while maintaining the same expected profit. The resulting TES size reduction from 14 to 10 hours translates into approximately up to $45.4 million in capital cost savings. The findings of this study can inform the ST-TES plant's design procedures and facilitate negotiations for electricity sales contracts.