Value Prediction (VP) is a microarchitectural technique that speculatively breaks data dependencies to increase the available Instruction Level Parallelism (ILP) in general purpose processors. Despite recent proposals, VP remains expensive and has intricate interactions with several stages of the classical superscalar pipeline. In this paper, we revisit and simplify VP by leveraging the irregular distribution of the values produced during the execution of common programs. First, we demonstrate that a reasonable fraction of the performance uplift brought by a full VP infrastructure can be obtained by predicting only a few “usual suspects” values. Furthermore, we show that doing so allows to greatly simplify VP operation as well as reduce the value predictor footprint. Lastly, we show that these Minimal and Targeted VP infrastructure conceptually enable Speculative Strength Reduction (SpSR), a rename-time optimization whereby instructions can disappear at rename in the presence of specific operand values.