Clinical trials with continuous primary endpoints typically measure outcomes at baseline, at a fixed timepoint (denoted T _min), and at intermediate timepoints. The analysis is commonly performed using the mixed model repeated measures method. It is sometimes expected that the effect size will be larger with follow-up longer than T _min. But extending the follow-up for all patients delays trial completion. We propose an alternative trial design and analysis method that potentially increases statistical power without extending the trial duration or increasing the sample size. We propose following the last enrolled patient until T _min, with earlier enrollees having variable follow-up durations up to a maximum of T _max. The sample size at T _max will be smaller than at T _min, and due to staggered enrollment, data missing at T _max will be missing completely at random. For analysis, we propose an alpha-adjusted procedure based on the smaller of the p values at T _min and T _max, termed $\mathit{\text{minP}}$. This approach can provide the highest power when the powers at T _min and T _max are similar. If the power at T _min and T _max differ significantly, the power of $\mathit{\text{minP}}$ is modestly reduced compared with the larger of the two powers. Rare disease trials, due to the limited size of the patient population, may benefit the most with this design.