An age replacement policy in a 1-unit system with minimal repairs is considered. The age of the system and the random cost of minimal repair is considered. The system is replaced at the first failure after age T. If it fails before age T, the repair cost is estimated and the system is minimally repaired if the estimated cost is less than L, otherwise, it is replaced. The optimal policy minimizing mean cost rate is discussed. An example is given with comparison to other replacement policies in the literature.