1. A processor, comprising: an associative memory including a plurality of ways organized in an asymmetric tree structure, each way including one or more memory elements, and the number of ways being other than a power of two; a replacement control unit, comprising circuitry to: cause, during execution of instructions and responsive to a miss in the associative memory while a decision node indicator points to a minority side of the asymmetric tree structure, the value of the decision node indicator to direct the next memory element replacement operation to a majority side of the asymmetric tree structure, the majority side of the asymmetric tree structure including more ways that are eligible to service a memory element replacement operation than the minority side of the asymmetric tree structure; determine, responsive to a miss in the associative memory while the decision node indicator points to the majority side of the asymmetric tree structure, whether or not to cause the value of the decision node indicator to direct the next memory element replacement operation to the minority side of the asymmetric tree structure dependent on a current replacement weight value.