Extinction is generally more context specific than acquisition, as illustrated by the renewal effect. While most strategies to counteract renewal focus on decreasing the context specificity of extinction, the present work aimed at increasing the context specificity of acquisition learning. Two experiments examined whether presenting cued reacquisition trials during extinction weaken renewal in human predictive learning. After acquisition in one context (AX) and extinction in another context (B), participants were given tests for renewal in a subset of the acquisition context (A) and the original acquisition context (AX). In Experiment 1, presentation of reacquisition trials during extinction, featured by a contextual cue from acquisition (X), weakened overall recovered responding in Context A but not in Context AX. In Experiment 2, we replicated our findings, but this time reacquisition training weakened renewed responding in Context A but not in Context AX. Most importantly, reacquisition training with a novel contextual cue (Y) did not weaken renewal (in A), suggesting that backward blocking effects increased the contextual control over acquisition performance. (Contains 1 table and 2 figures.)