Search models are used in a variety of fields. One of those is consumer search and in it the Stahl model is one of the most popular search models. The literature in search models concentrates mainly on equilibria with a consumer reserve price. This is a simplifying condition, which narrows down severely the freedom of the consumer. For example, once the model has a finite number of sellers who select different strategies a situation may arise where reserve price may not exist. This paper addresses the possibility of equilibria without reserve price, when sellers can use asymmetric strategies. Here a condition is given which ensures existence of reserve price in all equilibria. The condition involves prices where sellers set mass points, and undercutting those prices. The condition states that if a searcher is satisfied with such price, she should be satisfied also when a small discount is offered to that price. Assuming this, it is possible to concentrate only on equilibria with reserve price, and investigate also situations where the sellers are heterogeneous, or equilibria are not symmetric.